Exercise 9 Page 866

We want to find the average number of free throw attempts needed in order to make $3$ free throws in a row. In order to conduct a simulation, let's analyze the given information.

A basketball player makes $80\%$ of her free throws attempts.

We will begin by converting the percent to a fraction. This means that the basketball player makes $4$ out of $5$ attempted throws and $1$ throw is unsuccessful. This enables us to make a random number table. Let $1$ represent an unsuccessful free throw and the numbers from $2$ to $5$ represent successfully made free throws. In order to find the number of free throw attempts needed to make $3$ free throws in a row, we will use a table of random numbers from $1$ to $5.$ Now, let's count how many trials it took before producing $3$ numbers in a row that are not $1.$ The first such sequence is $4$ $4$ $3,$ which occurred after $9$ throws. Now we will look at a different table of random numbers from $1$ to $5.$ This time we get a sequence of $3$ numbers in a row that are not $1$ after $4$ throws. Since we are interested in the average number of free throws needed, we have to conduct this simulation a few more times. In this case, it took $7$ throws. Here, we see she needed $8$ trials. In this attempt, only $3$ free throws were needed. In order to find the average number of throws required to make $3$ free throws in a row, we need to calculate the mean of the trials from the tables. Therefore, about $6$ free throw attempts needed in order to make $3$ free throws in a row.