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
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:
$\displaystyle ^nC_0 (0.1)^0 (0.9)^{n} < 0.5 \Rightarrow (0.9)^n < 0.5 \Rightarrow n = 7$.
(b) done in a similar way (I get 29).