Question

A piñata is a container filled with candy and is broke by hitting it with a stick. The probability that Amanda will break a piñata on her first his is 0.58. She will continue to hit the piñata until it breaks. If she does not break the piñata on a particular hit, the piñata is weakened and the probability that she will break it on the next hit is 0.14 greater than the probability on the previous hit. For example, if the piñata does not break on the first hit, the probability that it will break on the second hit is 0.72 (found by 0.58 + 0.14 = 0.72). Calculate the probability that Amanda does not break the piñata on the first hit and does break the piñata on the second hit

Answer 1

0.3024

Explanation:

Given the following :

Probability of breaking pinata on first hit = 0.58;

P(first hit break) = 0.58

P(does not break on first hit) = 1 - p(first hit break) = 1 - 0.58 = 0.42

P(2nd hit break) = p(first hit break) + 0.14 = 0.58 + 0.14 = 0.72

Hence, Calculate the probability that Amanda does not break the piñata on the first hit and does break the piñata on the second hit

P(does not break on first hit) * p(2nd hit break)

0.42 * 0.72 = 0.3024