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:

.

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