Chapter 13.3, Problem 17AYU

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

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

To determine

The probability of getting a 2 or a 4, followed by Red.

Answer to Problem 17AYU

Probability of getting 2 or a 4, followed by Red is $\frac{1}{6}$.

Explanation of Solution

Given:

To spin spinner I, 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 a 2 or a 4 followed by red.

The sample space is $S=\{1Yellow,2Yellow,3Yellow,4Yellow,1Red,2Red,3Red,4Red,1Green,2Green,3Green,4Green\}$.

Each outcome is equally likely to occur; There are 12 outcomes.

Probability of getting 2 or a 4, followed by Red is given by $P\left(2Red\right)\text{ or }P\left(4Red\right)$,

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

$P\left(2Red\right)\text{ or }P\left(4Red\right)=P\left(2Red\right)+P\left(4Red\right)$

$P\left(2Red\right)\text{ or }P\left(4Red\right)=\frac{1}{12}+\frac{1}{12}$

$P\left(2Red\right)\text{ or }P\left(4Red\right)=\frac{2}{12}=\frac{1}{6}$