Answered

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 0.59. The probability that the Yankees win and

score 5 or more runs is 0.46. What is the probability that the Yankees would score 5 or more

runs when they lose the game? Round your answer to the nearest thousandth.

Verified Answer :

Answer: To solve this problem, we can use the formula for conditional probability:

(

∣

)

=

(

and

)

(

)

P(A∣B)=

P(B)

P(A and B)

​

Where:

(

∣

)

P(A∣B) is the probability of event A occurring given that event B has occurred.

(

and

)

P(A and B) is the probability of both events A and B occurring.

(

)

P(B) is the probability of event B occurring.

In this case:

Event A: Yankees score 5 or more runs.

Event B: The Yankees lose the game.

Given that the probability that the Yankees win and score 5 or more runs is 0.46, we have

(

and

)

=

0.46

P(A and B)=0.46.

Given that the probability that the Yankees will win a game is 0.56, we have

(

)

=

1

−

0.56

=

0.44

P(B)=1−0.56=0.44.

Now, we can plug these values into the formula to find

(

∣

)

P(A∣B):

(

∣

)

=

0.46

0.44

≈

1.045

P(A∣B)=

0.44

0.46

​

≈1.045

Rounding this to the nearest thousandth, we get approximately

1.045

1.045. However, probabilities cannot exceed 1, so the correct probability is 1.

Step-by-step explanation:

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