A cereal maker places a toy in each of its cereal boxes. The probability of winning this toy is 1 in 5. Find the probability that you

(a) win your first toy with your fifth purchase,

(b) win your first toy with your first, second, third, or fourth purchase, and

(c) do not win a toy with your first five 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.