Chapter 13.3, Problem 20AYU

In Problems 17-22, use the following spinners to construct a probability model for each experiment.

Spin spinner II, then I, then III. What is the probability of getting Yellow, followed by a 2 or a 4, followed by Forward?

To determine

The probability of getting Yellow, followed by a 2 or a 4, followed by Forward?

Answer to Problem 20AYU

$P\left(Yellow2Forward\right)orP\left(Yellow4Forward\right)=\frac{1}{12}$.

Explanation of Solution

Given:

Spin spinner II, then I, then III.

Formula used:

If $S$ is the sample space of this experiment,

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

Calculation:

To get Yellow, followed by a 2 or a 4, followed by Forward.

The sample space is $S=\{Yellow1Forward,Yellow2Forward,Yellow3Forward,Yellow4forward,Yellow1Backward,Yellow2Backward,Yellow3Backward,$ $Yellow4Backward,Red1Forward,Red2Forward,Red3Forward,Red4forward,Red1Backward,Red2Backward,Red3Backward,$ $Red4Backward,Green1Forward,Green2Forward,Green3Forward,Green4forward,Green1Backward,Green2Backward,Green3Backward,Green4Backward\}$.

Each outcome is equally likely to occur; There are 24 outcomes.

Probability of getting Yellow, followed by a 2 or a 4, followed by Forward,

$P\left(Yellow2Forward\right)orP\left(Yellow4Forward\right)$.

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

$P\left(Yellow2Forward\right)orP\left(Yellow4Forward\right)=P\left(Yellow2Forward\right)+P\left(Yellow4Forward\right)$.

$P\left(Yellow2Forward\right)orP\left(Yellow4Forward\right)=\frac{1}{24}+\frac{1}{24}=\frac{2}{24}=\frac{1}{12}$