Question

question
this season, the probability that the yankees will score 5 or more runs in a game is 0.54. the probability that the yankees will win a game is 0.49 and 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 5 or more runs? round your answer to the nearest thousandth.
answer attempt 1 out of 2
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Explanation:

Step1: Identify the formula for conditional probability

The formula for conditional probability is \( P(A|B) = \frac{P(A \cap B)}{P(B)} \), where \( A \) is the event that the Yankees win, and \( B \) is the event that the Yankees score 5 or more runs.
We know \( P(B) = 0.54 \) (probability of scoring 5 or more runs) and \( P(A \cap B) = 0.49 \) (probability of winning and scoring 5 or more runs).

Step2: Apply the conditional probability formula

Substitute the values into the formula: \( P(A|B) = \frac{0.49}{0.54} \).

Step3: Calculate the result and round

Calculate \( \frac{0.49}{0.54} \approx 0.907407 \). Round to the nearest thousandth, which is 0.907.

Answer:

0.907