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A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is 1/100, find the probability that he will win a prize 

(i) at least once 

(ii) exactly once 

(iii) at least twice.

1 Answer

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Best answer

Let X = number of winning prizes. 

p = probability of winning a prize

The p.m.f. of X is given by

(i) P(a person wins a prize at least once)

Hence, probability of winning a prize at least once = 1 – \(\left(\frac{99}{100}\right)^{50}\)

(ii) P(a person wins exactly one prize) = P[X = 1] = p(1)

Hence, probability of winning a prize exactly once = \(\frac{1}{2} \left(\frac{99}{100}\right)^{49}\)

(iii) P(a persons wins the prize at least twice) = P[X ≥ 2]

= 1 – P[X < 2]

= 1 – [p(0) + p(1)]

Hence, the probability of winning the prize at least twice = 1 – 149 \(\left(\frac{99^{49}}{100^{50}}\right).\)

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