Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Conditional probability:

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

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

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

$P(B|A) = \frac{0.41}{0.53} = 0.774$

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