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Question
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is 1/100. What is the probability that he will in a prize (a) at least once (b) exactly once (c) at least twice?
Solution
Let X represent the number of winning prizes in 50 lotteries. The trials are Bernoulli trials.
Clearly, X has a binomial distribution with n = 50 and p = 1/100
(a) P (winning at least once) = P (X ≥ 1)
(b) P (winning exactly once) = P(X = 1)
(c) P (at least twice) = P(X ≥ 2)
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