Question

A football team has a 70% chance of winning when it doesn’t snow, but only a 40% chance of winning when it does snow. Suppose there is 50% chance of snow. What is the probability given the team wins

Answer 1

To find the probability that the football team wins given that it snows, we can use conditional probability and Bayes' theorem.

Step-by-step explanation:

To find the probability that the football team wins given that it snows, we need to use conditional probability.

Let A be the event that the team wins, and B be the event that it snows. We want to find P(A|B), the probability that the team wins given that it snows.

Using Bayes' theorem, we can write:

P(A|B) = (P(B|A) * P(A)) / P(B)

Given that P(B) = 0.50 (50% chance of snow), P(A) = 0.70 (70% chance of winning without snow), and P(B|A) = 0.40 (40% chance of winning with snow), we can substitute these values into the equation to calculate P(A|B).

P(A|B) = (0.40 * 0.70) / 0.50 = 0.56

Therefore, the probability that the team wins given that it snows is 0.56 or 56%.