Chapter 13.3, Problem 22AYU

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

Spin spinner III, then spinner I twice. What is the probability of getting Forward, followed by a 1 or a 3, followed by a 2 or a 4?

To determine

What is the probability of getting forward, followed by a 1 or a 3, followed by a 2 or a 4?

Answer to Problem 22AYU

$P\left(Forward12\right)orP\left(Forward14\right)orP\left(Forward32\right)orP\left(Forward34\right)=\frac{1}{8}$.

Explanation of Solution

Given:

Spin spinner III, then spinner I twice.

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 $S=\{Forward11,Forward12,Forward13,Forward14,Forward21,Forward22,Forward23,$ $Forward24,Forward31,Forward32,Forward33,Forward34,Forward41,Forward42,Forward43,Forward44,Backward11,Backward12,Backward13,Backward14,$ $Backward21,Backward22,Backward23,Backward24,Backward31,Backward33,Backward32,Backward34,Backward41,Backward42,Backward43,Backward44\}$.

There are 32 equally likely events.

The probability of getting a Forward, followed by a 1 or a 3, followed by a 2 or a 4 is given below.

$E=\left\{Forward12,Forward32,Forward14,Forward34\right\}$

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

$n\left(S\right)=32$

$P\left(E\right)=\frac{4}{32}=\frac{1}{8}$