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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 0.56. The probability that the Yankees lose and score fewer than 5 runs is 0.36. What is the probability that the Yankees will win when they score fewer than 5 runs? Round your answer to the nearest thousandth.

0.182 probability that the Yankees will win when they score fewer than 5 runs

Step-by-step explanation:

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

In which

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

is the probability of both A and B happening.

P(A) is the probability of A happening.

In this problem:

When the Yankees score less than 5 runs, either they win, or they lose. The sum of these probabilities is 1.

Probability they lose:

Event A: Scoring fewer than 5 runs.

Event B: Losing

The probability that the Yankees will score 5 or more runs in a game is 0.56.

So 1 - 0.56 = 0.44 probability the Yankees score fewer than 5 runs.

This means that

The probability that the Yankees lose and score fewer than 5 runs is 0.36.

This means that

Then the probability they lose is:

Probability they win:

p + 0.818 = 1

p = 0.182

0.182 probability that the Yankees will win when they score fewer than 5 runs

c

step-by-step explanation: