Chapter 8.6, Problem 56E

(a).

To determine

To find:

The probability that the person selected is a person who does not favor the amendment.

Answer to Problem 56E

The required probability who does not in the favor of amendment is $0.45$ .

Explanation of Solution

Given:

The results of the study are listed in the table, where D represents Democrat and R represents Republican.

	D	R	Total
Favor	$23$	$32$	$55$
Oppose	$25$	$9$	$34$
Unsure	$7$	$4$	$11$
Total	$55$	$45$	$100$

Concept Used:

Apply the formula of the probability:

  $\begin{array}{c}P\left(A\right)=\frac{NumberofFavourableOutcome}{TotalNumberofFavourableOutcome}\\ =\frac{n\left(A\right)}{n\left(S\right)}\end{array}$

Calculation:

Total number of people interviewed is $100$ .

So, $n\left(S\right)=100$

Out of $100$ people $45\left(Oppose+Unsure\right)$ members were not in the favor of the amendment.

Thus, $n\left(A\right)=45$

So, the required probability who does not favor the amendment is:

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

Conclusion:

Hence, the required probability who does not in the favor of amendment is $0.45$ .

(b).

To determine

To find:

The probability that the person selected is a Republican.

Answer to Problem 56E

The required probability for the person who is Republican is $0.45$ .

Explanation of Solution

Given:

The results of the study are listed in the table, where D represents Democrat and R represents Republican.

	D	R	Total
Favor	$23$	$32$	$55$
Oppose	$25$	$9$	$34$
Unsure	$7$	$4$	$11$
Total	$55$	$45$	$100$

Concept Used:

Apply the formula of the probability:

  $\begin{array}{c}P\left(A\right)=\frac{NumberofFavourableOutcome}{TotalNumberofFavourableOutcome}\\ =\frac{n\left(A\right)}{n\left(S\right)}\end{array}$

Calculation:

Total number of people interviewed is $100$ .

So, $n\left(S\right)=100$

Out of $100$ people $45$ of the people interviewed were republican.

Thus, $n\left(A\right)=45$ .

So, the required probability is:

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

Conclusion:

Hence, the required probability for the person who is Republican is $0.45$ .

(c).

To determine

To find:

The probability that the person is selected is a Democrat who favors the amendment.

Answer to Problem 56E

The required probability for the person who is Democrats in favor of amendment is $0.23$ .

Explanation of Solution

Given:

The results of the study are listed in the table, where D represents Democrat and R represents Republican.

	D	R	Total
Favor	$23$	$32$	$55$
Oppose	$25$	$9$	$34$
Unsure	$7$	$4$	$11$
Total	$55$	$45$	$100$

Concept Used:

Apply the formula of the probability:

  $\begin{array}{c}P\left(A\right)=\frac{NumberofFavourableOutcome}{TotalNumberofFavourableOutcome}\\ =\frac{n\left(A\right)}{n\left(S\right)}\end{array}$

Calculation:

Total number of people interviewed is $100$ .

So, $n\left(S\right)=100$

Out of $100$ people $23$ of the people were Democrats in favor of the amendment.

Thus, $n\left(A\right)=23$ .

So, the required probability is:

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

Conclusion:

Hence, the required probability for the person who is Democrats in favor of amendment is $0.23$ .