a Suppose your probability of winning a certain game is 110

a. Suppose your probability of winning a certain game is 1/10. You play it 10 times. If successive plays are independent, what is the chance that you win at least once?

b. Repeat part a, but with n plays and 1/n as the probability of winning on each play.

c. What is the limit of the answer to part b as n increases to infinity?

Solution

a)

P(win at least one) = 1 - P(no win) = 1 - (1-1/10)^10

P(win at least one) = 0.65132156 [ANSWER]

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b)

P(win at least one) = 1 - P(no win) = 1 - (1-1/n)^n [ANSWER]

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b)

As

lim (1-1/n)^n = 1/e,
n-->oo

P(win at least one) = 1 - P(no win) = 1 - (1-1/n)^n

approaches,

P(Win at least 1, n-->oo) = 1 - 1/e [ANSWER]