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B. (5 points) It is claimed that for a particular lottery, 1/10 of the 50 million tickets will win a prize. Find the smallest number of tickets that must be purchased so that the probability of winning at least one prize is greater than 0.9 P: o. 1 .5 n-2
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Answer #1

Let X be a random variable denoting no. of winning tickets then X ~ Binomial(n, 1/10) According to the problem, P(X >1) > 0.9 Let f(n) (9/10)

For n=1,2,3,...,22

the values of f(n) are:

[0.9000, 0.8100, 0.7290, 0.6561, 0.5905, 0.5314, 0.4783, 0.4305, 0.3874, 0.3487,
0.3138, 0.2824, 0.2542, 0.2288, 0.2059, 0.1853, 0.1668, 0.1501, 0.1351, 0.1216,
0.1094, 0.0985

We see that when n=22, f(22)<0.1

Hence smallest n=22

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