A cereal maker places a game piece in each of its cereal boxes. The probability of winning a prize in the game is 1 in 4. Find the probability that you
(a) Win your first prize with your fourth purchase,
(b) Win your first prize with your first, second, or third purchase,
(c) Do not win a prize with your first four purchases.
Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.