Chapter 5.2, Problem 39E

(a)

To determine

To compute: Probability that a young adult has some education beyond high school but doesn’t have a bachelor’s degree.

Answer to Problem 39E

Probability that a young adult has some education beyond high school but doesn’t have a bachelor’s degree is 0.28.

Explanation of Solution

Given information:

Probability of the person who did not complete the high school $=0.\text{13}$

Probability of the person who completed the high school but no further education $=0.\text{29}$

Probability of the person who has at least bachelor degree $=0.\text{3}0$

Calculation:

As the sum of the probabilities is 1, so

  $\begin{array}{l}\text{Probability of the person who has someeducation after high school but does not have a bachelor}’\text{s degree }=\\ \text{1 }–\text{ P }\left(\text{who did not complete the high school}\right)–\text{ P }\left(\text{who completed the high school but no further education}\right)\\ –\text{P }\left(\text{who has at least bachelor degree}\right)\end{array}$

P (who has some education after high school but does not have a bachelor’s degree)

  $=\text{ 1 }–0.\text{13 }–0.\text{29}-0.\text{3}0=0.\text{28}$

(b)

To determine

To compute: Probability that an adult has completed high school.

Answer to Problem 39E

Probability that an adult has completed high school is 0.87.

Explanation of Solution

Formula used:

  $\begin{array}{l}\text{P }\left(\text{high school}\right)=\text{ P }\left(\text{completed highschool but no further education}\right)+\\ \text{P }\left(\text{at least bachelor}’\text{s degree}\right)+\text{ P}\left(\text{completed high school but does not have a bachelor}’\text{s degree}\right)\end{array}$

Concept used:

Addition of mutually exclusive events

As the event are disjoint or cannot occur simultaneously, they are mutually exclusive events.

Calculation:

P (high school) $=0.\text{29 }+0.\text{3}0+0.\text{28 }=0.\text{87}$

(c)

To determine

To compute: Probability that an adult has further education beyond high school.

Answer to Problem 39E

Probability that an adult has further education beyond high school is 0.58.

Explanation of Solution

Formula used:

  $\begin{array}{l}\text{P }\left(\text{further education beyond high school}\right)=\text{ P }\left(\text{at least bachelor}’\text{s degree}\right)+\\ \text{ P }\left(\text{completed high school but does not have a bachelor}’\text{s degree}\right)\end{array}$

Concept used:

Addition rule of mutually exclusive events

A person who has a bachelor’s degree must have completed high school and has further education.

Calculation:

P (further education beyond high school) $=0.\text{3}0+0.\text{28 }=0.\text{58}$