Question

The baseball team has a double-header on Saturday. The probability that they will win both games is 50%. The probability that they will win just the first game is 65%, What is the probability that the team will win the 2nd game given that they have already won the first game? (PLEASE SHOW YOU'RE WORK)

Answer 1

77%

Explanation:

Given the following :

Probability of winning both games = 50%

Probability of winning just the first game = 65%

Let the probability of winning the ;

First game = p(A) = 65%

Second game = p(B)

Both games = p(A and B) = 50%

What is the probability that the team will win the 2nd game given that they have already won the first game

The above question is a conditional probability question :

Probability of winning the second Given that they've already won the first = p(B | A)

p(B | A) = (A and B) / p(A)

p(B | A) = 50% / 65%

p(B | A) = 0.5 / 0.65

p(B | A) = 0.7692307

= 76.9% = 77%