a We want to find the experimental probability that a baseball player got a hit. We will use the actual results of an experiment and compare the number of times the event occurs to the number of times the experiment is done.
P = Times the event occurs/Times the experiment is done
In our case, the number of times that the experiment is done is the total number of times the player came up to bat, which is 64. The number of times that the events occurs is the number of hits the player got, which is equal to 19. We have enough information to calculate the desired probability.
P(got a hit) = Times the event occurs/Times the experiment is done
The experimental probability that the baseball player got a hit is about 0.297, or about 29.7 %.
b We want to estimate the number of hits the player is likely to get if he comes up to a bat 200 times in a season. To do so, we need to use the following formula.
Let's denote the number of hits the player is likely to get as h and the total number of times the player comes up to bat as b. This will enable us to rewrite the formula.
h = P(got a hit) * b
We know that the player will come up to bat 200 times in the season, so we can substitute 200 for b. The probability that the player will actually get a hit in the attempt is the probability found in Part A. This means that we can substitute 0.297 for P(got a hit).
