Question

One interpretation of a baseball player's batting average is as the empirical probability of getting a hit each time the player goes to bat. If a player with a batting average of 0.2560.256 bats 55 times in a game, and each at-bat is an independent event, what is the probability of the player getting at least on hit in the game

Answer 1

The probability of getting at least one hit in 5 games is 0.772

Explanation:

The correct question is as follows;

One interpretation of a baseball player's batting average is as the empirical probability of gettig a hit each time the player goes to bat. If a player witt a batting average of 0.256 bats 5 times in a game, and each at-bat is an independent event, what is the probability of the player getting at least one hit in the game?

We proceed with the answer as follows;

Here, we want to calculate the probability of a player with a certain batting average getting at least one hit in a game if he bats 5 times

Mathematically, Probability of getting at least one hit in 5 games = 1 - Probability of getting no hit in 5 games

Let p = probability of getting hit in a game = 0.256

q = Probability of getting no hit in a game = 1-0.256 = 0.744

So the probability of getting no hits in 5 games will be 0.744^5 = 0.228

Thus, the probability of getting at least one hit in the 5 games = 1 - 0.228 = 0.772