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)

=

10