We play a variation of monty hall the contestant is presented with curtains behind each there s a prize with

a prize with probability p independently of the other curtains. The player chooses one curtain (a) The game host tells the contestant there's a prize hiding behind at least one of the other curtains, and offers the player a chance to change his choice. Should he? (b) The game host tells the player there's a prize hiding behind exactly one of the other curtains. Should the player change his choice? How does your answer depend on p (c) How would your answer to section (b) change if there are n curtains in total? (d) Bonus (4 points): How would your answer to section (a) change if there are 4 curtains in total?