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This season, the probability that the Yankees will win a game is 0.52 and the probability that the Yankees will score 5 or more runs in a game is 0.6 . The probability that the Yankees lose and score fewer than 5 runs is 0.33 . 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 $0$ . $52$ and the probability that the Yankees will score $5$ or more runs in a game is $0$ . $6$ . The probability that the Yankees lose and score fewer than $5$ runs is $0$ . $33$ . 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: $\newline$

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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

.

52

and the probability that the Yankees will score

5

or more runs in a game is

0

.

6

. The probability that the Yankees lose and score fewer than

5

runs is

0

.

33

. 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:

\newline

Events Denoted: Let's denote the events as follows: $\newline$ $W$ : The Yankees win a game. $\newline$ $L$ : The Yankees lose a game. $\newline$ $S$ : The Yankees score $5$ or more runs in a game. $\newline$ We are given the following probabilities: $\newline$ $P(W) = 0.52$ $\newline$ $P(S) = 0.6$ $\newline$ $P(L \text{ and not } S) = 0.33$ $\newline$ We need to find the probability that the Yankees will lose when they score $5$ or more runs, which can be denoted as $P(L \text{ and } S)$ .
Find Losing Probability: First, we need to find the probability that the Yankees lose a game, which is the complement of the probability that they win. Since the probability of winning is $0.52$ , the probability of losing is: $\newline$ $P(L) = 1 - P(W)$ $\newline$ $P(L) = 1 - 0.52$ $\newline$ $P(L) = 0.48$
Calculate Losing and Scoring: Now, we can use the probability of losing and scoring fewer than $5$ runs to find the probability of losing and scoring $5$ or more runs. We can use the following relationship: $\newline$ $P(L) = P(L \text{ and } S) + P(L \text{ and not } S)$ $\newline$ We already know $P(L)$ and $P(L \text{ and not } S)$ , so we can solve for $P(L \text{ and } S)$ : $\newline$ $P(L \text{ and } S) = P(L) - P(L \text{ and not } S)$ $\newline$ $P(L \text{ and } S) = 0.48 - 0.33$ $\newline$ $P(L \text{ and } S) = 0.15$
Round Final Probability: Finally, we round the answer to the nearest thousandth as requested: $P(L \text{ and } S) \approx 0.150$

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