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Math Help - Lottery probability

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    Lottery probability

    It is claimed that for a particular lottery, 1/10 of the 50,000,000 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 (a) 0.50, (b) 0.95
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    Quote Originally Posted by antman View Post
    It is claimed that for a particular lottery, 1/10 of the 50,000,000 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 (a) 0.50, (b) 0.95
    Let X be the random variable number of winning tickets.

    Since the population is large, you can assume the X ~ Binomial(n = ?, p = 0.1) where n is the number of tickets you buy.

    (a) Calculate the smallest positive value of n such that Pr(X > 0) > 0.5 => 1 - Pr(X = 0) > 0.5 => Pr(X = 0) < 0.5:

    ^nC_0 (0.1)^0 (0.9)^{n} < 0.5 \Rightarrow (0.9)^n < 0.5 \Rightarrow n = 7.


    (b) done in a similar way (I get 29).
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