Question

This probability distribution shows the typical distribution of pitches thrown to a batter in a given at bat in a baseball game. Find the probability that the pitcher will throw fewer than 3 pitches to a batter.

Answer 1

0.35

Explanation:

This probability distribution is shown below:

Pitch 1 2 3 4 5

Frequency 15 20 40 15 10

Probability 0.15 0.2 0.4 0.15 0.1

The probability that the pitcher will throw fewer than 3 pitches to a batter = P(X < 3)

X is the number of pitches thrown. Therefore:

P(X < 3) = P(X = 1) or P(X = 2)

The additive rule pf probability states that if two events X and Y are dependent events, the probability of X or Y occurring is the sum of their individual probability.

P(X < 3) = P(X = 1) or P(X = 2) = P(X = 1) + P(X = 2) = 0.15 + 0.2 = 0.35

The probability that the pitcher will throw fewer than 3 pitches to a batter = 0.35