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This season, the probability that the Yankees will win a game is 0.54 and the probability that the Yankees will score 5 or more runs in a game is 0.51 . The probability that the Yankees lose and score fewer than 5 runs is 0.38 . What is the probability that the Yankees will lose when they score 5 or more runs? Round your answer to the nearest thousandth.
Answer:

This season, the probability that the Yankees will win a game is $0$ . $54$ and the probability that the Yankees will score $5$ or more runs in a game is $0$ . $51$ . The probability that the Yankees lose and score fewer than $5$ runs is $0$ . $38$ . What is the probability that the Yankees will lose when they score $5$ or more runs? Round your answer to the nearest thousandth. $\newline$ Answer:

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Find probabilities using the addition rule

Full solution

Q. This season, the probability that the Yankees will win a game is

0

.

54

and the probability that the Yankees will score

5

or more runs in a game is

0

.

51

. The probability that the Yankees lose and score fewer than

5

runs is

0

.

38

. What is the probability that the Yankees will lose when they score

5

or more runs? Round your answer to the nearest thousandth.

\newline

Answer:

Events Denoted: Let's denote the events as follows: $\newline$ W: The Yankees win a game. $\newline$ S: The Yankees score $5$ or more runs in a game. $\newline$ L: The Yankees lose a game. $\newline$ F: The Yankees score fewer than $5$ runs in a game. $\newline$ We are given the following probabilities: $\newline$ $P(W) = 0.54$ $\newline$ $P(S) = 0.51$ $\newline$ $P(L \text{ and } F) = 0.38$ $\newline$ We need to find the probability that the Yankees will lose when they score $5$ or more runs, which can be denoted as $P(L \text{ and } S)$ . $\newline$ First, we need to find the probability that the Yankees lose a game, which is the complement of the probability that they win a game. $\newline$ $P(L) = 1 - P(W)$ $\newline$ $P(L) = 1 - 0.54$ $\newline$ $P(L) = 0.46$
Find Probabilities: Next, we need to find the probability that the Yankees score fewer than $5$ runs, which is the complement of the probability that they score $5$ or more runs. $\newline$ $P(F) = 1 - P(S)$ $\newline$ $P(F) = 1 - 0.51$ $\newline$ $P(F) = 0.49$
Calculate Intersection: Now, we can use the probability of the Yankees losing and scoring fewer than $5$ runs to find the probability of them losing and scoring $5$ or more runs. $\newline$ We can use the formula for the intersection of two events: $\newline$ $P(L \text{ and } S) = P(L) - P(L \text{ and } F)$ $\newline$ Substituting the given values, we get: $\newline$ $P(L \text{ and } S) = 0.46 - 0.38$ $\newline$ $P(L \text{ and } S) = 0.08$

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