Chapter 13.8, Problem 5CYU

To determine

To calculate: Probability the spinner will land on $6$ after the first spin and on $6$ after the second spin.

Answer to Problem 5CYU

Probability of getting $6$ in single spinner is $\frac{1}{8}$ .

Probability of getting $6$ on first spin and $6$ on second spin is $\frac{1}{64}$ .

Explanation of Solution

Given information:

A spinner with $8$ equal sections labeled $1-8$ is spun twice.

So total outcomes are $=1,2,3,4,5,6,7,8$

Event $A$ is spinner will land on $6$ after the first spin.

Event $B$ is Probability of getting $6$ on first spin and $6$ on second spin

Calculation:

As per given information,

Total outcomes $=8nos$

Favorable outcome $=1nos$

Probability of getting $6$

1. in single spinner,
Now, divide the number of possible outcomes by total outcomes.

So,

  $\begin{array}{l}P\left(A\right)=\frac{S\left(A\right)}{S\left(P\right)}\\ =\frac{1}{8}\end{array}$

Therefore, Probability of getting $6$ in single spinner is $\frac{1}{8}$ .

Probability of getting $6$ on first spin and $6$

1. on second spin,
Now, divide the number of possible outcomes by total outcomes.

So,

  $\begin{array}{l}P\left(A\right)=\frac{S\left(B\right)}{S\left(P\right)}\\ =\frac{1}{8}.\frac{1}{8}\\ =\frac{1}{64}\end{array}$

Therefore, Probability of getting $6$ on first spin and $6$ on second spin is $\frac{1}{64}$ .