Chapter 13.3, Problem 21AYU

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

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

To determine

What is the probability of getting a 2, followed by a 2 or a 4, followed by Red or Green?

Answer to Problem 21AYU

$P\left(22Red\right)orP\left(22green\right)orP\left(24Red\right)orP\left(24green\right)=\frac{1}{12}$.

Explanation of Solution

Given:

Spin spinner I twice, 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:

The sample space $S=\{11Yellow,12Yellow,13Yellow,14Yellow,21Yellow,22Yellow,23Yellow,24Yellow,31Yellow,32Yellow,33Yellow,34Yellow,11Yellow,12Yellow,13 Yellow,14Yellow,$ $11Red,12Red,13Red,14Red,21Red,22Red,23Red,24Red,31Red,32Red,33Red,34Red,11Red,12Red,13Red,14Red,$ $11Green,12Green,13Green,14Green,21Green,22Green,23Green,24Green,31Green,32Green,33Green,34Green,11Green,12Green,13Green,14Green\}$.

There are 48 equally likely events.

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

$E=\{22Red,24Red,22Green,24Green\}$

$n\left(E\right)=4$

$n\left(S\right)=48$

$P\left(E\right)=\frac{4}{48}=\frac{1}{12}$