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 0.57. The probability that the Yankees win and score 5 or more runs is 0.38. What is the probability that the Yankees lose and score fewer than 5 runs? Round your answer to the nearest thousandth.

0.33

Step-by-step explanation:

We can think of this in tems of a venn diagram.

We have a rectangle, which represents the probabilities combined, which is 1.

Then we have two interlocking circles, the first representing the probability the yankees win, the second representing the probability the yankes score 5 or more runs, and the overlap representing the probability of both.

Therefore, the probability of losing and scoring less than 5 runs must be the area outside the circles but inside the rectangle.

The union of 'winning' and 'scoring 5 or more runs' is equal to the sum of the probability of either, minus the probability of both, which is 0.48+0.57-0.38 = 0.67.

Therefore the probability neither happen is 1-0.67 = 0.33