Chapter 9.7, Problem 37E

a.

To determine

To find: probability that a student selected at random from the class is going to college.

Answer to Problem 37E

  $\frac{13}{16}$

Explanation of Solution

Given:

In a high school graduating class of 128 students, 52 are on the honor roll. Of these, 48 are going on to college. Of the 76 students not on the honor roll, 56 are going on to college.

The given data can be summarized in the following table:

	Go to college	Doesn’t go to college	Total
Honor roll	48	$52-48=4$	52
Not on honor roll	56	$76-56=20$	76
Total	$48+56=104$	$4+20=24$	128

Let E be the event that a student chosen at random is going to college.

Then $n\left(E\right)=104$

Total number of students in class is $n\left(S\right)=128$

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

  $\begin{array}{c}P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}\\ =\frac{104}{128}\\ =\frac{13}{16}\end{array}$

b.

To determine

To find: probability that a student selected at random from the class is not going to college.

Answer to Problem 37E

  $\frac{3}{16}$

Explanation of Solution

Given:

In a high school graduating class of 128 students, 52 are on the honor roll. Of these, 48 are going on to college. Of the 76 students not on the honor roll, 56 are going on to college.

The given data can be summarized in the following table:

	Go to college	Doesn’t go to college	Total
Honor roll	48	$52-48=4$	52
Not on honor roll	56	$76-56=20$	76
Total	$48+56=104$	$4+20=24$	128

Let F be the event that a student chosen at random is not going to college.

Then $n\left(F\right)=24$

Total number of students in class is $n\left(S\right)=128$

Thus, the probability that a student selected at random from the class is not going to college is:

  $\begin{array}{c}P\left(F\right)=\frac{n\left(F\right)}{n\left(S\right)}\\ =\frac{24}{128}\\ =\frac{3}{16}\end{array}$

c.

To determine

To find: probability that a student selected at random from the class is not going to college and on the honor roll.

Answer to Problem 37E

  $\frac{1}{32}$

Explanation of Solution

Given:

In a high school graduating class of 128 students, 52 are on the honor roll. Of these, 48 are going on to college. Of the 76 students not on the honor roll, 56 are going on to college.

The given data can be summarized in the following table:

	Go to college	Doesn’t go to college	Total
Honor roll	48	$52-48=4$	52
Not on honor roll	56	$76-56=20$	76
Total	$48+56=104$	$4+20=24$	128

Let G be the event that a student chosen at random is not  not going to college and on the honor roll.

Then $n\left(G\right)=4$

Total number of students in class is $n\left(S\right)=128$

Thus, the probability that a student selected at random from the class is  not going to college and on the honor roll is:

  $\begin{array}{c}P\left(G\right)=\frac{n\left(G\right)}{n\left(S\right)}\\ =\frac{4}{128}\\ =\frac{1}{32}\end{array}$