Chapter 9, Problem 96RE

a.

To determine

To find: probability that a person selected at random from the sample is a person who opposes the proposal.

Answer to Problem 96RE

  $\frac{52}{125}$

Explanation of Solution

The given data is summarized in the following table:

	Students	Faculty	Admin	Total
Favor	237	37	18	292
Oppose	163	38	7	208
Total	400	75	25	500

Let E be the event that person selected at random from the sample is a person who opposes the proposal.

Then $n\left(E\right)=208$

Total number of people surveyed in college is $n\left(S\right)=500$

Thus, the probability that person selected at random from the sample is a person who opposes the proposal is:

  $\begin{array}{c}P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}\\ =\frac{208}{500}\\ =\frac{52}{125}\end{array}$

b.

To determine

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

Answer to Problem 96RE

  $\frac{4}{5}$

Explanation of Solution

The given data is summarized in the following table:

	Students	Faculty	Admin	Total
Favor	237	37	18	292
Oppose	163	38	7	208
Total	400	75	25	500

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

Then $n\left(F\right)=400$

Total number of people surveyed in college is $n\left(S\right)=500$

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

  $\begin{array}{c}P\left(F\right)=\frac{n\left(F\right)}{n\left(S\right)}\\ =\frac{400}{500}\\ =\frac{4}{5}\end{array}$

c.

To determine

To find: probability that a person selected at random from the sample is a faculty member who favors the proposal.

Answer to Problem 96RE

  $\frac{37}{500}$

Explanation of Solution

The given data is summarized in the following table:

	Students	Faculty	Admin	Total
Favor	237	37	18	292
Oppose	163	38	7	208
Total	400	75	25	500

Let G be the event that person selected at random from the sample is a faculty member who favors the proposal.

Then $n\left(G\right)=37$

Total number of people surveyed in college is $n\left(S\right)=500$

Thus, the probability that person selected at random from the sample is a faculty member who favors the proposal is:

  $\begin{array}{c}P\left(G\right)=\frac{n\left(G\right)}{n\left(S\right)}\\ =\frac{37}{500}\end{array}$