The probability that an event will occur is what is the probability that the event will not occur a

MBA course. The university knows that the probability of a student completing the course successfully is 80%. We take a random sample of 4, independent students. a. What is the probability exactly 0 students complete the course? b. What is the probability exactly 1 student complete the course? c. What is the probability exactly 2 students complete the course? d. What is the probability exactly 3 students complete the course? e. What is the probability 3 or (all) 4 of the students complete the course? f. What is the expected number of students (out of the 4 sampled) that complete the course? g. What is the standard deviation of the number of students that complete the course?

first 2 weeks. 50 people who joined the programme are sampled, their weight loss is 9 pounds with a standard deviation of 2.8 pounds. Can we conclude at the .05 level that a person joining the programme will lose less than 10 pounds? (2) The following is a random sample of 90-day futures prices in dollars for 1 troy oz. of silver from The Wall Street Journal issues in May and June of 1997: 4.74, 4.77, 4.87, 4.91, 4.83, 4.72, 4.92, 4.86, 4.97, 4.71, 4.90, 4.93, 4.75, 4.88, 4.79, 4.83, 4.89. Required: a. Calculate the mean b. Median c. Standard deviation of the 90-day future price of silver data (3) A mining company needs to estimate the average amount of copper ore per ton mined. A random sample of 50 tons gives a sample mean of 146,75 pounds. The population standard deviation is assumed to be 35.2 pounds. Required: a. Give a 95% confidence interval for the average amount of copper in the population of tons mined. b. Give a 90% confidence interval for the average amount of coper per ton c. Give a 99% confidence interval for the average amount of coper per ton (4) An e-commerce Website gets 2,385 visitors on a particular day. Among these, 1790 visitors explore the products by looking at more pages at the site. Among these 1790 visitors who explore the products, 387 make a purchase. Required: a. If a visitor chosen at random from all those who visited the site, what is the probability that the visitor explored the products b. If a visitor is chosen at random from all those who visited the site, what is the probability that the visitor made a purchase. c. If a visitor is chosen at random from all those who explored the products, what is the probability that the visitor made a purchase. d. Which of the preceding three probabilities is relevant to the design of the home page that leads to product page.

particular micro-organism. She finds that 62% of the samples have at least one micro-organism present. Assuming the micro- organisms are randomly occurring, with an average rate of occurrence, a) estimate k, the average number of micro-organisms per sample. b) what is the probability that in the combined sea water of three samples (15ml) she finds more than 2 micro-organisms?

When selecting one card from a standard deck, what is the probability of selecting a Jack AND a Club? An urn contains 10 red balls, 6 green balls, 15 orange balls, and 14 blue balls. If one ball is randomly drawn from the urn, what are the odds against the ball being green? The odds against an event are 7 to 1. Find the probability that the event will occur? The probability of an event is 7/10. Find the odds against that event.

, determine the probability that a randomly selected score will be between a 450 and 700.

thing else. The probability a player makes a free throw in an away game is 50%, independently of everything else. Half of the games are home games. What is the probability that when the player throws two free throws she will make both? Assuming the player makes the first free throw, what is the probability she will make the second? Are the two events independent? Assuming that the player made both free throws, what is the probability it was a home game?

of Sport-Equip Ltd, a company that sells sports equipment. Some of the users who visit the website end up buying sports equipment from the website while others are simply browsing in order to obtain product information. (a) Clearly explain and justify which probability distribution you would use to describe the number of Internet users who visit the website of Sport-Equip Ltd in a one hour period. [There is no need to calculate any probabilities for this part of the question] (5 marks) (b) What is the probability that during any half-hour period, there will be less than 3 visitors to the website? (5 marks) (c) What is the probability that during any two-hour period, there will be more than 15 visitors to the website? (5 marks) (d) If a user has just visited the website, find the probability that the website will have another visitor within the next 10 minutes. In your answer, state the probability distribution you have used and explain your choice. (4 marks) (e) It is estimated that 40% of Internet users who visit Sport-Equip Ltd’s website buy a product from the company. If 100 users visit the website over a given period of time, find the probability that more than 50 of them will buy a product from the company. In your answer, state the probability distribution you have used and explain your choice

. If there is an​ intruder, system A sounds an alarm with probability 0.85 and system B sounds an alarm with probability 0.95. If there is no​ intruder, system A sounds an alarm with probability 0.20 and system B sounds an alarm with probability 0.15 . ​Now, assume that the probability of an intruder is 0.4 . If both systems sound an​ alarm, what is the probability that there is an​ intruder?

y aces or twos, you lose the game immediately. You also lose if you draw picture cards(J,Q,K) more than twice. In this question, you’ll study the probability of winning this game.(a) What is the probability of drawing no aces or twos after thirteen draws?(b) Given you have drawn thirteen times, none of which is aces or twos, what is the probability that you draw at most two picture cards?(c) What is the probability to win this game? 12. Suppose you are tossing an unbiased coin for100times.(a) What is the probability of getting50heads and50tails?(b) LetXbe the random variable counting the number of heads you observe in this exper-iment. What is the expected value ofX? What is the variance ofX? What is thestandard deviation ofX? 13. The following are probability distributions for two random variablesX,Y. kPr(X=k) 0,0.4 1,0.3 2,0.3 kPr(Y=k) 0,0.5 1,0.3 2,0.2 (a) Construct the probability distribution table for the random variableXY.(b) Find E[X],E[Y] and E[XY]. Is is true that E[XY] =E[X]E[Y]?(c) Find the variances σ2X,σ2Y,σ2XY of X,Y and XY. Is it true that σ2XY=σ2Xσ2Y? 14. The aliens who are fond of gambling came back to play another game with you. In this game, you first toss a coin5times. If you observe3or fewer tails, you roll a die3times. If youobserve4or more tails, you roll a die20times. What is the probability that you end up with at most two6’s in your dice rolls? 15. (Challenge question, worth2points) You have two bags, each of which contains10marbles.Each time you remove a marble from a random bag. What is the probability that after one of the bags is emptied, there are still exactly3marbles in the other bag?

- 1); I{x>1}, theta > 1. (a) Show that log Xi has an exponential distribution with a mean of 1/theta. (b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0. (c) Give formula for nding the rejection region for a given value of alpha. Hint: use the result from (a) to find the distribution of the test statistic. (d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}. (e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0. (f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.

- 1); I{x>1}, theta > 1. (a) Show that log Xi has an exponential distribution with a mean of 1/theta. (b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0. (c) Give formula for nding the rejection region for a given value of alpha. Hint: use the result from (a) to find the distribution of the test statistic. (d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}. (e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0. (f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.

- 1); I{x>1}, theta > 1. (a) Show that log Xi has an exponential distribution with a mean of 1/theta. (b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0. (c) Give formula for nding the rejection region for a given value of alpha. Hint: use the result from (a) to find the distribution of the test statistic. (d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}. (e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0. (f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.

2,3,4,7). If it lands tails, a fair six-sided die is thrown (with values 3,4,5,6,7,9). Regardless of which die is used, Alice eats n grains of rice, where n is the largest prime factor of the die result (for example, the largest prime factor of 9 is 3). (a) What is the conditional probability that the coin lands heads, given that Alice eats three grains of rice? (b) Suppose that the entire experiment is conducted twice on the following day (starting with a new coin toss on the second run-through). What is the conditional probability that the coin lands heads on both run-throughs, given that Alice eats a total of five grains of rice during the two run-throughs? (Do not count the two grains from part (a) in part (b); we assume two brand new experiments, each with a new coin toss. Start your solution by defining a suitable partition of the sample space. Please use an appropriate notation and/or justification in words, for each value that you give as part of your solution.) Exercise 5) Alice and Bob throw an unfair coin repeatedly, with probability 2/5 of landing heads. Alice starts with £2 and Bob starts with £3 . Each time the unfair coin lands heads, Alice gives Bob £1 . Each time the unfair coin lands tails, Bob gives Alice £1 . The game ends when one player has £5 . (a) Draw a labelled Markov chain describing the problem, and write down a transition matrix P. Write down the communication classes, and classify them as either recurrent or transient. (b) Using the transition matrix, calculate the probability that Alice loses all of her money in exactly four tosses of the unfair coin. (c) Calculate the (total) probability that Alice loses all of her money (before Bob loses all of his). (d) Calculate the expected (mean) number of tosses of the unfair coin, for the game to end.

tosses (i.e. the second, fourth, sixth etc.) are heads? (b) In an infinite series of independent coin tosses, what is the probability that the first heads is followed by a tails?

two objects and recorded whether or not the dog being tested correctly chose the object indicated. A four-year-old male beagle named Augie participated in this study. He chose the correct object 42 out of 70 times when the experimenter leaned towards the correct object. (a) (2 points) Let the parameter of interest, π, represent the probability that the long-run probability that Augie chooses correctly. Researches are interested to see if Augie understands human body cues (better than gussing). Fill in the blanks for the null and alternative hypotheses. H0 : Ha : (b) (6 points) Based on the above context, conduct a test of significance to determine the p-value to investigate if domestic dogs understand human body cues. What conclusion will you draw with significance level of 10%? (If you use an applet, please specify which applet you use, and the inputs.) (c) (5 points) Based on the above context, conduct a test of significance to determine the p-value to investigate if domestic dogs understand human body cues. What conclusion will you draw with significance level of 5%? (If you use an applet, please specify which applet you use, and the inputs.) (d) (2 points) Are your conclusions from part (b) and (c) the same? If they are different, please provide an explanation. (e) (5 points) Shown below is a dotplot from a simulation of 100 sample proportions under the assump- tion that the long-run probability that Augie chooses correct is 0.50. Based on this dotplot, would a 90% confidence interval for π contain the value 0.5? Explain your answer. (f) (4 points) Compute the standard error of the sample proportion of times that Augie chose the object correctly. 1 (g) (5 points) (h) (3 points) question? (i) (4 points) (j) (4 points) A. B. C. Construct an approximate 95% confidence interval for π using the 2SD method. What is the margin of error of the confidence interval that you found in the previous How would you interpret the confidence interval that you found in part (g)? Which of the following is a correct interpretation of the 95% confidence level? If Augie repeats this process many times, then about 95% of the intervals produced will capture the true proportion of times of choosing the correct objective. About 95% times Augie chooses the correct objective. If Augie repeats this process and constructs 20 intervals from separate independent sam- ples, we can expect about 19 of those intervals to contain the true proportion Augie chooses the correct objective. (k) (4 points) object 21 out of 35 times. Conjecture how, if at all, the center and the width of a 99% confidence interval would change with these data, compared to the original 2SD 95% confidence interval. The center of the confidence interval would . The width of the confidence interval would . (l) (4 points) Suppose that we repeated the same study with Augie, and this time he chose the correct object 17 out of 35 times, and we also change the confidence level from 95% to 99%. Conjecture how, if at all, the center and the width of a 99% confidence interval would change with these data, compared to the original 2SD 95% confidence interval. Suppose that we repeated the same study with Augie, and this time he chose the correct The center of the confidence interval would The width of the confidence interval would . .

nd standard deviation 6 inches. A button hyperlink to the SALT program that reads: Use SALT. (a) What is the probability that an 18-year-old man selected at random is between 64 and 66 inches tall? (Round your answer to four decimal places.) Correct: Your answer is correct. (b) If a random sample of seven 18-year-old men is selected, what is the probability that the mean height x is between 64 and 66 inches? (Round your answer to four decimal places.) Incorrect: Your answer is incorrect. (c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this? The probability in part (b) is much higher because the standard deviation is smaller for the x distribution. The probability in part (b) is much higher because the standard deviation is larger for the x distribution. The probability in part (b) is much higher because the mean is smaller for the x distribution. The probability in part (b) is much higher because the mean is larger for the x distribution. The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.

es them to perform a task. Assuming that all of the times are different, how many different rankings are possible?"

on a subsample of weekly data from Randall’s Supermarket, one of the biggest in the UK. Randall’s marketing management team wishes to identify trends and patterns in a sample of weekly data collected for a number of their loyalty cardholders during a 26-week period. The data includes information on the customers’ gender, age, shopping frequency per week and shopping basket price. Randall’s operates two different types of stores (convenient stores and superstores) but they also sell to customers via an online shopping platform. The collected data are from all three different types of stores. Finally, the data provides information on the consistency of the customer’s shopping basket regarding the type of products purchased. These can vary from value products, to brand as well as the supermarket’s own high-quality product series Randall’s Top. As a business analyst you are required to analyse those data, make any necessary modifications in order to determine whether for any single customer it is possible to predict the value of their shopping basket. Randall’s marketing management team is only interested in identifying whether the spending of the potential customer will fall in one of three possible groups including: • Low spender (shopping basket value of £25 or less) • Medium Spender (shopping basket value between £25.01 and £70) and • High spenders (shopping basket greater than £70) For the purpose of your analysis you are provided with the data set Randall’s.xls. You have to decide, which method is appropriate to apply for the problem under consideration and undertake the necessary analysis. Once you have completed this analysis, write a report for the Randall’s marketing management team summarising your findings but also describing all necessary steps undertaken in the analysis. The manager is a competent business analyst himself/herself so the report can include technical terms, although you should not exceed five pages. Screenshots and supporting materials can be included in the appendix. Requirements After completing your analysis, you should submit a report that consists of two parts. Part A being a non-technical summary of your findings and Part B a detailed report of the analysis undertaken with more details. Part A: A short report for the Head of Randall’s Marketing Management (20 per cent). This should briefly explain the aim of the project, a clear summary and justification of the methods considered as well as an overview of the results. Although, the Head of Randall’s Marketing Management team who will receive this summary is a competent business analytics practitioner, the majority of the other team members have little knowledge of statistical modelling and want to know nothing about the technical and statistical underpinning of the techniques used in this analysis. This report should be no more than two sides of A4 including graphs, tables, etc. In this report you should include all the objectives of this analysis, summary of data and results as well as your recommendations (if any). Part B: A technical report on the various stages of the analysis (80 per cent). The analysis should be carried out using the range of analytics tools discussed: • SPSS Statistics Ensure that the exercise references: • Binary and multinomial logistic regression • Linear vs Logistic regression • Logit Model with odds Ratio • Co-efficients and Chi Squared • MLR co-efficients • Assessing usefulness of MLR model • Interpreting a model • Assessing over-all model fit with Psuedo R-Squared measures • Classification accuracy (Hit Ratio) • Wald Statistic • Odd ratio exp(B) • Ratio of the probability of an event happening vs not happening • Ratio of the odds after a unit change in the predictor to the original odds • Assumptions • Residuals analysis • Cook’s distance • DfBeta • Adequacy (with variance inflation factor VIF and tolerance statistic) • Outliers and influential points cannot just be removed. We need to check them (typo? – unusual data?) • Check for multicollinearity • Parsimony Write a short and concise report to explain the technical detail of what you have done for each step of the analysis. The report should also cover the following information: • Any type of analysis that might be useful and check whether the main assumptions behind the analyses do not hold or cannot be • Give evidence of the understanding of the statistical tools that you are using. For example, comment on the model selection procedure and the coefficient interpretation, e.g. comment on the interpretation of the logistic regression coefficients if such a method is used and provide an example of • Conclusions and explanation, in non-technical terms, of the main points

n electronic circuit contains five such components wired in such a way that the circuit works as long as at least one of the components works. What is the probability that the lifetime of the circuit is at least eight years? Explain what assumptions you make in order to carry out your calculation.

Leaf and 6 of the employees are vegetarian and own a Nissan Leaf. If you randomly select an employee from company XYZ, what is the probability that the employee is vegetarian or that she/he owns a Nissan Leaf?

is the probability of an individual phone being defective? If a quality control engineer wants to carefully analyze a defective mobile phone, what is the probability of her getting at least one defective phone in a lot of 25? Is the probability high enough that the engineer can be reasonably sure of getting a defective mobile phone that can be used for her analysis?

f the students make their choices independently and each is as likely to pick one integer as any other, what is the probability that 8 or more will select 4,5 or 6? b Having observed eight students who selected 4, 5, or 6, what conclusion do you draw based on your answer to part (a)?A missile protection system consists of n radar sets operating independently, each with a probability of .9 of detecting a missile entering a zone that is covered by all of the units. a If n = 5 and a missile enters the zone, what is the probability that exactly four sets detect the missile? At least one set? b How large must n be if we require that the probability of detecting a missile that enters the zone be .999?

ross income of over $80,000. What is the probability that of 15 such returns, at most four will be audited? Ans = 0.142

100 and a standard deviation of 15. a. What is the probability that a given applicant will score over 100? b. Determine the probability that a random applicant scores over 135. c. Determine the probability that an applicant scores between 85 and 135.

k of 10 cards numbered 1-10. I draw 5 cards (each time i draw i put the card back and shuffle). The numbers were 8, 2, 4, 9, and 4. What is the probability that it will be 4 on the 6th time i draw? I know each card has a 10% chance of being drawn. I also know the probability of a 10% event happening twice is 1%. But wouldnt the odds be lower since i drew 4 a couple trials earlier? How exactly would i calculate that. If there is an online calculator that executes the answer id like to know. Just a college student who craves probability. :)

IRS employee randomly selects and checks 10 forms for mistakes. What is the probability that exactly one has an error?

incomplete dominance. The intermediate phenotype is pink flowers. Based on the following Punnett Square, what is the probability that an offspring will be homozygous dominant?

ng n distinct integers in just his thoughts. He plays turns on the list. In each turn he does the following– He takes a number (in its index’s order ) and swap it with any number in the list including itself i.e. if it swap it with itself it doesn’t move at all (The selection of the number is completely random). He does the same for all the elements in their index’s order in that turn. If initially the list was unsorted, such that, no element was in sorted position, then find the probability that the list is sorted after m such turns. Note : Take the assumption that if an element is not in its sorted position then it can be in any other n − 1 positions equally likely.

Elena will win an upset victory in a best of five chess tournament

odule. If all paths are equally likely, what would be the probability of choosing a path that begins with an up move and ends with an up move? (each path is made up of moves that either go up one unit or over one unit to the right).

the larger the group gets. At what number of people does it become more likely than not that there will be at least one 1%er?

h of them. The probability that he makes a mistake in his thinking is 0.005. The probability that an assistant gives wrong information is 0.3. Assuming that the mistakes made by the manager are independent of the information given by the assistants, find the probability that he reaches a wrong decision.

and how to solve: “A history lecture hall class has 15 students. There is a 15% absentee rate per class meeting. Find the probability that exactly one student will be absent from class.” I already know that: n = 15 p = 15% q = 1 - 15 = 1 - 0.15 = 0.85 ...and then you do: p (x = 1) = C 15 & 1 and then... (0.15)^1 (0.85)^14 Please help me understand the rest. Thank you!

weighing between 140 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 145 lb and a standard deviation of 29.9 lb. a. If a pilot is randomly​ selected, find the probability that his weight is between 140 lb and 191 lb.

et loans (he doesn't "earn" income). With the loans (L) he needs to decide between first period consumption (C1) and investment (I). The amount invested will allow him to get a second period income Y with probability P which is increasing in I (therefore, P(I)), In case of success and the person obtain Y, the individual should use Y to repay the loan (L) that he requested in the first period and consume in the second period (C2). However, with probability 1 - P(I), the person don't get Y and therefore only consume C1. Note that if the individual only invest the loan (L=I) and don't obtain Y, he can't consume anything. That motivates him not to invest the whole loan and keep part of the loan in order to warrant at least first period consumption. Therefore, considering B the parameter for the time preference, the problem would be: max U=ln(C1) + Bln(C2) s.t: L = I + C1 Y(I) = L(1+r) + C2 with Probability P(I) or s.t: L = I + C1 with probability 1 - P(I) My question is, Have you ever seen something like this? If yes, how to proceed? What is more important, I really need a bibliography (a book or article talking about this)

36 Using your knowledge of probability, why should Nizar have known that his answer was NOT correct and gone back to review his calculations? 2. A four-colored spinner was spun 80 times. The spinner landed on green 15 times, yellow 30 times, blue 10 times, and red 25. Based on this data, what is the experimental probability of the spinner landing on green? (Write your answer as a fraction in lowest terms.) 3. If the probability that a certain mechanical part in your new car will fail this year is 0.05, what is the probability that the mechanical part will not fail this first year? 4. A coin is loaded so that the probability of getting tails is 1/4. If the coin is flipped twice, what is the probability of getting tails twice? 5.If a 6-sided die is tossed and then a coin is flipped, what is the probability that an odd number is rolled and the coin lands on heads? 6.A field goal kicker makes 3 of every 7 attempts at a field goal. If he kicks 4 field goals in a certain game, what is the probability that he'll make all four? (Write your answer as a fraction in lowest terms.)

2)(x - 3)(x + 3) d. (x2 - 4)(x2+ 9) Value: 1 The table below shows the cost of purchasing a standard stapler at five office supply stores, A through E. If the median cost of purchasing a standard stapler for these stores was $17.99, which of the following could NOT have been the cost of the stapler for Store A? staplergraph.jpg a. $19.95 b. $18.95 c. $16.95 d. $19.25 Value: 1 If equation image indicator then x = a. 7 b. 1/5 c. 5 d. 1/7 Value: 1 A six−sided die, with sides numbered 1,2, 3,4,5, and 6, is tossed. What is the probability of tossing a number less than three? a. 1/3 b. 0 c. 1/2 d. 1/4 Value: 1 If 6m + 4 = 8m, then 4m = a. 6 b. 2 c. 8 d. 4 Value: 1 In the xy-plane, what is the y-intercept of the graph of the equation equation image indicator? a. 2 b. 4 c. 16 d. There is no y-intercept. Value: 1 Which of the following equations has both 2 and −4 as solutions? a. x2 + 6x + 8 = 0 b. x2 - 2x - 8 = 0 c. x2 + 2x - 8 = 0 d. x2 - 2x + 8 = 0 Value: 1 The perimeter of a square is 20 ft. If you increase the length of the square by 2 feet and decrease the width by 1 foot, what is the area, in square feet, of the new figure? a. 22 b. 28 c. 35 d. 40 Value: 1 (3x-2y4)-3 = a. equation image indicator b. equation image indicator c. equation image indicator d. equation image indicator Value: 1 A softball is tossed into the air upward from a first floor balcony. The distance of the ball above the ground at any time is given by the function, distance function.png, where h(t) is the height of the softball above the ground (in feet) and t is the time (in seconds). What was the maximum height, in feet, of the softball above the ground after it was thrown? a. 28 b. 30 c. 32 d. 34 Value: 1 A group of 100 people, some students and some faculty, attended a museum opening. Each student paid $10 per person for entrance to the museum and each of the faculty paid $25 per person for entrance. If the total paid, for all 100 people, was $1300, how many students attended the museum opening? a. 20 b. 50 c. 70 d. 80 Value: 1 The ratio of Sam's age to Hank's age is 5 to 3. If the sum of their ages is 24, how old is Hank? a. 21 b. 15 c. 19 d. 9 Value: 1 In the xy−coordinate plane shown below, point P has coordinates (8, −6). Which of the following is an equation of the line that contains points O and P? O and P graph.jpg a. equation image indicator b. equation image indicator c. equation image indicator d. equation image indicator Value: 1 The variables x and y are inversely proportional, and y = 2 when x = 3. What is the value of y when x = 9? a. 54 b. 6 c. 2/3 d. 3/2 Value: 1 A farmer has 1235 trees to be planted on a rectangular parcel of land. If there are 24 trees planted in each row and each row must be complete before it is planted, how many trees will be left over after planting? a. 21 b. 11 c. 0 d. 55

is a multiple of three or greater than eight. A certain game consist of rolling a single fair die and pays off as follows nine dollars for a six, six dollars for a five, one dollar for four and no payoffs otherwise.Find the expected winnings for this game. A fair die is rolled four times. A 6 is considered success While all other outcomes are failures find the probability of three successes. A pet store has nine puppies including 4 poodles 3 terriers and 2 retrievers. If Rebecca an errand in that order each select one puppy at random without replacement find the probability that Aaron select a retriever given that from last Rebecca selects a poodle. Experience shows that a ski lodge will be for (166 guests) if there is a heavy snowfall in December, well only partially full (52 guests) With a light snowfall. What is the expected number of guests if the probability for a heavy snowfall is 0.40? I assume that heavy snowfall and light snowfall are the only two possibilities. A pet store has six puppies Including two poodles two Terriers and to retrievers. If Rebecca and Aaron in that order each select one puppy random with replacement (They both may select the same one) Find the probability That Rebecca selects a terrier and Aaron selects a retriever. Three married couples arrange themselves randomly in six consecutive seats in a row. Determine (A) the number of ways the following event can occur, And (B) the probability of the event. (The denominator of the probability fraction will be 6!=720, The total number of ways to arrange six items ). Each man was that immediately to the right of his wife. A coin is tossed five times. Find the probability that all our heads. Find the probability that at least three are heads. A certain prescription drug is known to produce undesirable facts and 35% of all patients due to drug. Among a random sample of a patient using a drug find the probability of the stated event. Exactly 5 have undesired effects. 10,000 raffle tickets are sold. One first prize of 1600, for second prizes of 800 each, And 9/3 prizes of 300 each or to be awarded with all winners selected randomly. If you purchase one ticket what are your expected winnings. Suppose a charitable organization decides to Raise money by raffling A trip worth 500. If 3000 tickets are sold at one dollar each find the expected net winnings for a person who buys one ticket. Round to the nearest cent Three men and seven women are waiting to be interviewed for jobs. If they are selected in random order find the probability that all men will be interviewed first A fair diet is rolled. What is the probability of rolling on our number or a number less than three. The pet store has 15 puppies, including five poodles, five Terriers, and five retrievers. If Rebecca and Aaron, in that order, select one puppy at random without replacement, find the probability that both select a poodle Beth is taking a nine question multiple-choice test for which each question Has three answer choices, only one of which is correct. Beth decides on answering By rolling a fair die And making the first answer choice if the die shows one or two, The second If the die shows three or four, and the third if the die shows five or six. Find the probability of the stated event. Exactly 6 correct answers For the experiment of drawing a single card from a standard 52 card deck find (a) the probability and (b) the odds are in favor that they do not drive six

r player at the table is showing a 5 and 6. Compute the expected value of a one-dollar insurance bet under these circumstances Question 2: Suppose that( perhaps after being hit one or more times) you have cards addings up to 18. Using the table provided in these notes, compute the probability that you will lose, and the probability that you will tie. Question 3: The "Royal Hand" consists of King and Queens of the same suit. Compute the probability of being dealt a Royal Hand in the first two cards. Question 4: Compute the probability that you will initially be dealt two cards adding up to exactly 20. ( First think about how many ways two cards can up to 20 in blackjack.) Question 5: You have two 9s in your hand. The dealer is showing a 7, and the only other player at the table is sowing a King and a 9. If you ask to be hit, what is the probability that you will bust on the next card?