Chapter 11, Problem 27E

To determine

To Calculate: the number of points researchers would score in a one-and-one situation.

Explanation of Solution

The knowledge that a player has made 72 percent of his foul shots this season is given. The number of points that researchers will receive in a one-to-one scenario must be calculated, meaning that the player gets a shot, and then a second shot only if the first one is taken by the researcher.

It is presumed that the likelihood that the player will score 1 point is 72%; thus, the likelihood that he will score 0 points is 28% (1 00%-72%). In addition, by multiplying by 2 the 72% likelihood that the researcher will make a shot, it will calculate the probability that the player will score both shots. Hence, 0.52 percent (0.72 percent multiplied by 2 shots) is the likelihood that the player can score 2 points.

Now, by taking the sum of the result of the points scored and their probabilities, it can compute the average points scored by the player in a one-to-one scenario.

  $\begin{array}{c}\text{Points = 1 Point }\times \text{ Probability +2 point }\times \text{Probability + 0 points}\times \text{Probability}\\ \text{=1 }\times \text{72\%}\text{+}\text{2}\times \text{0}\text{.52\% + 0 }\times 2\text{8\%}\\ \text{=1}\text{.76}\end{array}$

Hence, in a one-to-one scenario, the player would score, on average, 1.76 points.