Chapter 9.7, Problem 38E

a.

To determine

To find: the probability that a class of 2016 alumnus selected at random is female.

Answer to Problem 38E

  $0.54$

Explanation of Solution

Given:

A college sends a survey to members of the class of 2016. Of the 1254 people who graduated that year, 672 are women, of whom 124 went on to graduate school. Of the 582 male graduates, 198 went on to graduate school.

The given data can be summarized in the following table:

	went on to graduate school	Doesn’t went to graduate school	Total
Female	124	$672-124=548$	672
Male	198	$582-198=384$	582
Total	$124+198=322$	$548+384=932$	1254

Let E be the event that alumnus selected at random is female.

Then $n\left(E\right)=672$

Total number of students in class is $n\left(S\right)=1254$

Thus, the probability that a student selected at random from the class is going to college is female is:

  $\begin{array}{c}P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}\\ =\frac{672}{1254}\\ \approx 0.54\end{array}$

b.

To determine

To find: the probability that a class of 2016 alumnus selected at random is male.

Answer to Problem 38E

  $0.46$

Explanation of Solution

Given:

A college sends a survey to members of the class of 2016. Of the 1254 people who graduated that year, 672 are women, of whom 124 went on to graduate school. Of the 582 male graduates, 198 went on to graduate school.

The given data can be summarized in the following table:

	went on to graduate school	Doesn’t went to graduate school	Total
Female	124	$672-124=548$	672
Male	198	$582-198=384$	582
Total	$124+198=322$	$548+384=932$	1254

Let F be the event that alumnus selected at random is male.

Then $n\left(F\right)=582$

Total number of students in class is $n\left(S\right)=1254$

Thus, the probability that a student selected at random from the class is going to college is male is:

  $\begin{array}{c}P\left(F\right)=\frac{n\left(F\right)}{n\left(S\right)}\\ =\frac{582}{1254}\\ \approx 0.46\end{array}$

c.

To determine

To find: the probability that a class of 2016 alumnus selected at random is Female and did not attend graduate school.

Answer to Problem 38E

  $0.44$

Explanation of Solution

Given:

A college sends a survey to members of the class of 2016. Of the 1254 people who graduated that year, 672 are women, of whom 124 went on to graduate school. Of the 582 male graduates, 198 went on to graduate school.

The given data can be summarized in the following table:

	went on to graduate school	Doesn’t went to graduate school	Total
Female	124	$672-124=548$	672
Male	198	$582-198=384$	582
Total	$124+198=322$	$548+384=932$	1254

Let G be the event that alumnus selected at random is Female and did not attend graduate school.

Then $n\left(G\right)=548$

Total number of students in class is $n\left(S\right)=1254$

Thus, the probability that a student selected at random from the class is going to college is Female and did not attend graduate school is:

  $\begin{array}{c}P\left(G\right)=\frac{n\left(G\right)}{n\left(S\right)}\\ =\frac{548}{1254}\\ \approx 0.44\end{array}$