Question
This season, the probability that the Yankees will win a game is o. 6 and the probability that the
Yankees will score 5 or more runs in a game is o.55. The probability that the Yankees lose and
score fewer than 5 runs is 0.29 . What is the probability that the Yankees will lose when they
score fewer than 5 runs? Round your answer to the nearest thousandth.
Answer
Yankees will score 5 or more runs in a game is o.55. The probability that the Yankees lose and
score fewer than 5 runs is 0.29 . What is the probability that the Yankees will lose when they
score fewer than 5 runs? Round your answer to the nearest thousandth.
Answer
Ask by Hodgson Rogers. in the United States
Mar 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability that the Yankees will lose when they score fewer than 5 runs is approximately 0.644.
Solution
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Extra Insights
To find the probability that the Yankees will lose when they score fewer than 5 runs (denote this as P(Loss | <5 runs)), we can use the formula for conditional probability:
We know from the problem that:
- P(Loss ∩ < 5 runs) = 0.29
Now we need to determine P(< 5 runs). We can find this by considering the total probability of the Yankees losing or winning. The total probability is 1, and we know:
- P(Win) = 0.6 → hence, P(Loss) = 1 - P(Win) = 0.4
- The probability of scoring 5 or more runs is 0.55, thus P(< 5 runs) = 1 - 0.55 = 0.45.
Now, substituting these values into the conditional probability formula:
Calculating this gives:
Rounding to the nearest thousandth, the answer is:
0.644.
