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

The probability of scoring fewer than 5 runs when they win is P = 0.19

How to find the probability?

We know that:

• The probability of winning a game is p = 0.53
• The probability of scoring 5 or more runs is q = 0.59
• The probability of winning and scoring  5 or more runs is k = 0.43

Notice that the joint probability is different than the product of the individual probabilities, this means that the events are not independent.

So, we know that the probability of winning is 0.53

Now, given that they win, the probability of scoring 5 or more times will be q' such that:

0.53*q' = 0.43

q' = 0.811

This means that when they win, the probability of scoring more than 5 times is 0.81

Then the probability of scoring less than 5 times when they win is 1 minus the above probability:

P = 1 - 0.81 = 0.19

The probability of scoring fewer than 5 runs when they win is P = 0.19

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