Chapter 6.7, Problem 10E

To determine

To find : the expected number of times the spinner stops on 8.

Answer to Problem 10E

Expected number of times the spinner stops on 8 is 12 or 13 times if it is spins 100 times.

Explanation of Solution

Given information :

The spinner spins 100 times.

Calculation :

Since, they are 8 equal divisions on the spin, so to total number of possible outcome is 8.

Also, if the spinner stops at 8, then number of favourable outcome will be 1 only.

Therefore, probability that the spinner stop at 8 in one spin is

  $\begin{array}{l}P\left(\text{Stops at 8}\right)=\frac{\text{Number of favourable outcome}}{\text{Number of possible outcome}}\\ P\left(\text{Stops at 8}\right)=\frac{\text{1}}{\text{8}}\end{array}$

Now, if the spinner spins 100 times, then multiply the probability of spinner stops at 8 in one spin with the number of spin to get how many times it stops at 8. Therefore,

  $\frac{1}{8}\times 100=12.5$

Hence,

Expected number of times the spinner stops on 8 is 12 or 13 times if it is spins 100 times.