Question
Question This season, the probability that the Yankees will win a game is 0.48 and the probability that the Yankees will score 5 or more runs in a game is 0.6 . The probability that the Yankees win and score 5 or more runs is 0.38. What is the probability that the Yankees will win when they score fewer than 5 runs? Round your answer to the nearest thousandth. Answer Attemptiout of 2 square
Solution
4.6
(326 Votos)
Mariana
Mestre · Tutor por 5 anos
Resposta
To find the probability that the Yankees will win when they score fewer than 5 runs, we can use the formula for conditional probability:
where:-
is the event that the Yankees win.-
is the event that the Yankees score fewer than 5 runs.First, we need to determine \( P(B) \), the probability that the Yankees score fewer than 5 runs. We know that:
Therefore, the probability that the Yankees score fewer than 5 runs is:
Next, we need to find \( P(A \cap B) \), the probability that the Yankees win and score fewer than 5 runs. We know that:
Therefore, the probability that the Yankees win and score fewer than 5 runs is:
Given that \( P(\text{Yankees win}) = 0.48 \):
Now, we can use the conditional probability formula:
Therefore, the probability that the Yankees will win when they score fewer than 5 runs is
.