Chapter 9.7, Problem 36E

a.

To determine

To find: probability that a person selected at random from the sample is a person who does not favor the amendment.

Answer to Problem 36E

  $0.34$

Explanation of Solution

The given data is summarized in the following table:

	Favor	Not Favor	Unsure	Total
D	23	25	7	55
R	32	9	4	45
Total	55	34	11	100

Let E be the event that person selected at random from the sample is a person who does not favor the amendment.

Then $n\left(E\right)=34$

Total number of people surveyed is $n\left(S\right)=100$

Thus, the probability that person selected at random from the sample is a person who does not favor the amendment is:

  $\begin{array}{c}P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}\\ =\frac{34}{100}\\ =0.34\end{array}$

b.

To determine

To find: probability that a person selected at random from the sample is a Republican.

Answer to Problem 36E

  $0.45$

Explanation of Solution

The given data is summarized in the following table:

	Favor	Not Favor	Unsure	Total
D	23	25	7	55
R	32	9	4	45
Total	55	34	11	100

Let F be the event that person selected at random from the sample is a Republican.

Then $n\left(F\right)=45$

Total number of people surveyed is $n\left(S\right)=100$

Thus, the probability that person selected at random from the sample is a Republican is:

  $\begin{array}{c}P\left(F\right)=\frac{n\left(F\right)}{n\left(S\right)}\\ =\frac{45}{100}\\ =0.45\end{array}$

c.

To determine

To find: probability that a person selected at random from the sample is a Democrat who favors the amendment.

Answer to Problem 36E

  $0.23$

Explanation of Solution

The given data is summarized in the following table:

	Favor	Not Favor	Unsure	Total
D	23	25	7	55
R	32	9	4	45
Total	55	34	11	100

Let G be the event that person selected at random from the sample is a Democrat who favors the amendment.

Then $n\left(G\right)=23$

Total number of people surveyed is $n\left(S\right)=100$

Thus, the probability that person selected at random from the sample is a Democrat who favors the amendment is:

  $\begin{array}{c}P\left(G\right)=\frac{n\left(G\right)}{n\left(S\right)}\\ =\frac{23}{100}\\ =0.23\end{array}$