Chapter 6.8, Problem 14E

To determine

To find : the probability that both spinner A and B stops on the same number in all four spins, when spinner A and B spins two times each.

Answer to Problem 14E

The probability that both spinners stop on the same number in all four spin is $\frac{\text{1}}{100}$ .

Explanation of Solution

Given information :

Consider, the information provided in the question,

The spinner B is divided into 5 equal parts namely 1, 2, 3, 4 and 5 and spinner B is divided into 4 equal parts namely 1, 2, 3, and 4.

Calculation :

Since, spinner A is divided into 5 parts and spinner B is divided into 4 parts. And if it is spun two times each then total number of possible outcome is $5\times 5\times 4\times 4=400$ .

Now, to stop on same number the spinner should stop either on 1, 2, 3, or 4. Thus, number of favourable outcome is 4. Therefore, the probability that both spinner stops on the same number in all four spin is

  $\begin{array}{l}P\left(\text{Stops on same number on all 4 spin}\right)=\frac{\text{Number of favaourable outcome}}{\text{Total number of outcome}}\\ P\left(\text{Stops on same number on all 4 spin}\right)=\frac{\text{4}}{400}\\ P\left(\text{Stops on same number on all 4 spin}\right)=\frac{\text{1}}{100}\end{array}$

Hence,

The probability that both spinner stops on the same number in all four spin is $\frac{\text{1}}{100}$ .