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 win a prize

(a) At least once


(b) Exactly once


(c) At least twice?


(a) In this question, let X represents the number of prizes winning in 50 lotteries and the trials are Bernoulli trials

Here clearly, we have X is a binomial distribution where n = 50 and


Thus,






Hence, probability of winning in lottery atleast once


= 1 – P (X <1)


= 1 – P (X = 0)





(b) Probability of winning in lottery exactly once





(c) Probability of winning in lottery atleast twice


= 1 – P (X < 2)








=


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