A baseball team has 4 pitchers and 4 catchers, all of whom play in a given game. The team manager records a defensive success if at least 2 of the pitchers and 3 of the catchers make no mistakes. In a given game, a pitcher makes no mistakes with probability .6 independently of any other player and a catcher makes no mistakes with probability .7. Give an exact expression for the probability that a randomly observed game is recorded as a success.

Question

Quizplus · Accepted Answer

The Answer of A baseball team has 4 pitchers and 4 catchers, all of whom play in a given game. The team manager records a defensive success if at least 2 of the pitchers and 3 of the catchers make no mistakes. In a given game, a pitcher makes no mistakes with probability .6 independently of any other player and a catcher makes no mistakes with probability .7. Give an exact expression for the probability that a randomly observed game is recorded as a success.

A Baseball Team Has 4 Pitchers and 4 Catchers, All