Answer:
0.226 = 22.6% probability that the Yankees will lose when they score 5 or more runs
Step-by-step explanation:
Conditional probability:
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
If the Yankees score 5 or more runs, either they win, or they lose. The sum of these probabilities is 1.
Probability that the Yankees win:
Event A: Scoring 5 or more runs.
Event B: Winning
The probability that the Yankees will score 5 or more runs in a game is 0.53.
This means that
The probability that the Yankees win and score 5 or more runs is 0.41.
This means that
So
0.774 probability that the Yankees will win when they score 5 or more runs
What is the probability that the Yankees will lose when they score 5 or more runs?
p + 0.774 = 1
p = 1 - 0.774
p = 0.226
0.226 = 22.6% probability that the Yankees will lose when they score 5 or more runs