Chapter 13.3, Problem 18AYU

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

Spin spinner III, then spinner II. What is the probability of getting Forward, followed by Yellow or Green?

To determine

The probability of getting forward, followed by Yellow or Green?

Answer to Problem 18AYU

$P\left(ForwardYellow\right)orP\left(ForwardGreen\right)=\frac{1}{3}$.

Explanation of Solution

Given:

To Spin spinner III, then spinner II.

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 Forward, followed by Yellow or Green.

The sample space is $S=\{ForwardYellow,ForwardRed,ForwardGreen,BackwardYellow,BackwardRed,BackwardGreen\}$.

Each outcome is equally likely to occur; There are 6 outcomes.

Probability of getting Forward followed by Yellow or Green is given by,

$P\left(ForwardYellow\right)orP\left(ForwardGreen\right)$.

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

$P\left(ForwardYellow\right)orP\left(ForwardGreen\right)=P\left(ForwardYellow\right)+P\left(ForwardGreen\right)$.

$P\left(ForwardYellow\right)orP\left(ForwardGreen\right)=\frac{1}{6}+\frac{1}{6}=\frac{1}{3}$.