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:
