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 0.52. The probability that the Yankees win and score 5 or more runs is 0.4. What is the probability that the Yankees lose and score fewer than 5 runs

And we can solve for the probability of interest and we got:

And if we replace the values given we got:

Step-by-step explanation:

For this case we define some notation:

A= The event that the Yankees will win a game

B= The event that the Yankees will score 5 or more runs in a game

We have defined the probabilities for these two events:

We also know the probability that the Yankees win and score 5 or more runs given by:

And we are interested on the probability that the Yankees lose and score fewer than 5 runs.

For this case we can use the total probability rule given by:

And we can solve for the probability of interest and we got:

And if we replace the values given we got:

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