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If i roll two dices there is a chance of rolling two equal numbers if i roll two dices

 
 

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1.If I roll two dices there is a 1/6 chance of rolling two equal numbers. If I roll two dices ...

(a second throw), what is the odds of getting two equals then?
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2.Hello, I have a problem calculating probability for a certain thing that happened. I'll try and make it sound like ...

it sound like a math problem. The problem : What are the chances of a 4 sided die landing on 1 twice and on 2 twice out of 4 rolls. The solution I came up with originally was (2/4) x (2/4) x (2/4) x (2/4) . Which I realized was wrong as this allowed the die to land on 1 four times in a row. So then I came up with this soultion (which i still think is wrong) (2/4) x (2/4) x (1/4) x (1/4) . So the reasoning behind this is : The first roll obviously has a 50% chance to roll on either 1 or 2. Second roll is the same. BUT, lets say both of them land on 1, and now it HAS to land on 2 the remaining two times. So my problem is with the current solution that I have is what if the die lands on 1 on the first roll, then on two for the second one. then the third roll would still have a 2/4 AKA a 50% chance of landing on either one. I'm sure the last roll is 1/4 but I just dont know if the order matters on the rolls. This has been driving me crazy the last hour. Please help if you can thanks
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

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