Question

This season, the probability that the Yankees will win a game is 0.53 and the probability that the Yankees will score 5 or more runs in a game is 0.59. The probability that the Yankee s win and score 5 or more runs is 0.43. What is the probability that the Yankees would score fewer than 5 runs when they win the game? Round your answer to the nearest thousandth .

Answer 1

Answer:

The probability is 0.244

Step-by-step explanation:

let A be the event that they win the game and B that the score 5 or more runs in a game. Then we are given the following

$P(A) =0.53, P(B) = 0.59, P(A\cap B) = 0.43$

We are asked for the following probability $P(A|B^c)$. Recall the following probability's properties

$P(A|B) = \frac{P(A\cap B)}{P(B)}$

$P(A) = 1-P(A^c)$

$P(A) = P(A\cap B^c) + P(A\cap B)$

From the last property we have that

$P(A\cap B^c) = P(A) -P(A\cap B)$

Then,

$P(A|B^c) = \frac{P(A\cap B^c)}{P(B^c)} = \frac{P(A)-P(A\cap B)}{1-P(B)} = \frac{0.53-0.43}{0.41} = 0.244$

Answer 2

Answer:

Step-by-step explanation: