Question

Problem 2 catcher's mitt before it leaves Foster's fingers! If the team wins a game then the probability that Foster was pitching is 0.8 but only if Foster had at least one day's rest since his last pitching assignment. If Foster does not have a day off and the team still wins, the probability that Foster was pitching drops by half of what it was on the previous day. If the team wins three games in succession from the Toronto Tachyons and Foster pitched in game #2, what is the probability that he pitched in one or more of the other games? (Assume that Foster did not pitch before the first game of this three game series.) Our star pitcher, Foster Enlight, can throw a pitch so fast that it gets to the on the day

Answer 1

Probability that Foster pitched in the first game = 0.8

Probability that Foster pitched in the second game = 0.4

Probability that Foster pitched in the third game = 0.2

Now, probability that Foster pitched in one or more of the other games, given that he pitched in game #2

= P(he pitched in exactly one of the first and third games) + P(he pitched in both the first and third games)

= P(he pitched in first game but not in third game) + P(he pitched in third game but not in first game) + P(he pitched in both the first and third games)

= 0.8*(1 - 0.2) + 0.2*(1 - 0.8) + 0.8*0.2

= 0.84

Thus, the required probability is 0.84