Suppose that 2% of cereal boxes contain a prize and the other 98% contain the message, "sorry, try again." consider the random v
ariable x, where x = number of boxes purchased until a prize is found. (round all answers to four decimal places.) (a) what is the probability that at most three boxes must be purchased? p(at most three boxes) = (b) what is the probability that exactly three boxes must be purchased? p(exactly three boxes) = (c) what is the probability that more than three boxes must be purchased? p(more than three boxes) =
<span>a) This is the sum of the probabilities of winning in 1, 2 or 3 boxes.
0.02 + (0.98*0.02) + (0.98*0.98*0.02) = 0.0588
b) Exactly three boxes requires the first two to lose.
(0.98*0.98*0.02) = 0.0192
c) This is the complement of answer for a).
1-.0588 = .9412</span>
