Question

This season, the probability that the Yankees will win a game is 0.49 and the

probability that the Yankees will score 5 or more runs in a game is 0.53. The
probability that the Yankees win and score 5 or more runs is 0.41. What is the
probability that the Yankees will lose when they score 5 or more runs? Round your
answer to the nearest thousandth.

Answer 1

0.226 = 22.6% probability that the Yankees will lose when they score 5 or more runs

Explanation:

Conditional probability:

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

If the Yankees score 5 or more runs, either they win, or they lose. The sum of these probabilities is 1.

Probability that the Yankees win:

Event A: Scoring 5 or more runs.

Event B: Winning

The probability that the Yankees will score 5 or more runs in a game is 0.53.

This means that
`P(A) = 0.53`

The probability that the Yankees win and score 5 or more runs is 0.41.

This means that
`P(A \cap B) = 0.41`

So

`P(B|A) = (0.41)/(0.53) = 0.774`

0.774 probability that the Yankees will win when they score 5 or more runs

What is the probability that the Yankees will lose when they score 5 or more runs?

p + 0.774 = 1

p = 1 - 0.774

p = 0.226

0.226 = 22.6% probability that the Yankees will lose when they score 5 or more runs