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This season, the probability that the Yankees will win a game is 0.56 and the probability that the Yankees will score 5 or more runs in a game is 0.61. The probability that the Yankees lose and score fewer than 5 runs is 0.32. What is the probability that the Yankees will lose when they score fewer than 5 runs? Round your answer to the nearest thousandth.

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jaycejax2006
1278 explains I want answers

The probability that the Yankees will lose when they score fewer than 5 runs is 0.821 (nearest to the thousandth).

What is the chain rule in probability for two events?

For two events A and B:

The chain rule states that the probability that A and B both occur is given by:

[tex]P(A \cap B) = P(A)P(B|A) = P(B)P( A|B)[/tex]

Lets suppose here that:

  • A = event that Yankees win a game
  • B = event that Yankees will score ≥ 5 in a game

Suppose A' and B' are their complementary events, then we have:

  • A' = event that Yankees will lose a game
  • B' = event that Yankees will score < 5 in game

Then, by the given data, we have:

[tex]P(A) = 0.56\\P(B) = 0.61\\P(A' \cap B') = 0.32[/tex]

We've to find [tex]P(A' | B')[/tex]

Using chain rule, we have:

[tex]P(A'|B') = \dfrac{P(A' \cap B')}{P(B')}[/tex]

Since P(B') = 1-P(B) = 100.61 = 0.39, therefore, we get:

[tex]P(A'|B') = \dfrac{P(A' \cap B')}{P(B')} = \dfrac{0.32}{0.39} \\\\P(A'|B') \approx 0.821[/tex]

Thus, the probability that the Yankees will lose when they score fewer than 5 runs is 0.821

Learn more about probability here:

brainly.com/question/1210781

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