Chapter 5.2, Problem 40E

(a)

To determine

Probability for college graduate customer but not currently employed.

Answer to Problem 40E

Probability for college graduate unemployed customer is 0.40.

Explanation of Solution

Given information:

20% are undergraduate students in business.

15% are undergraduate students in other fields of study.

60% college graduates are currently employed.

Calculations:

According to the complement rule,

  $P\left({\text{A}}^c\right)=P\left(\text{not}\text{A}\right)=1-P\left(\text{A}\right)$

Let

A: Undergraduate students in business

B: Undergraduate students in other fields of study

C: College graduate who is currently employed

Note that

Probability for college graduate who is currently employed,

  $P\left(\text{C}\right)=60\%=0.60$

Apply complement rule:

  $\begin{array}{l}P\left({\text{C}}^c\right)=P\left(\text{not}\text{C}\right)=1-P\left(\text{C}\right)\\ =1-0.60\\ =0.40\end{array}$

Thus,

Probability that the customer is a college graduate who is not currently employed is 0.40.

(b)

To determine

Probability for an undergraduate customer.

Answer to Problem 40E

Probability for an undergraduate customer is 0.35.

Explanation of Solution

Given information:

20% are undergraduate students in business.

15% are undergraduate students in other fields of study.

60% college graduates are currently employed.

Calculations:

According to addition rule for mutually exclusive events:

  $P\left(\text{A}\cup \text{B}\right)=P\left(\text{A}\text{or}\text{B}\right)=P\left(\text{A}\right)+P\left(\text{B}\right)$

Let

A: Undergraduate students in business

B: Undergraduate students in other fields of study

C: College graduate who is currently employed

Note that

Probability for undergraduate in business,

  $P\left(\text{A}\right)=20\%=0.20$

Probability for undergraduate in other field,

  $P\left(\text{B}\right)=15\%=0.15$

Undergraduate refers to the undergraduate students in business or undergraduate students in other fields of study.

Thus,

The symbolic representation for undergraduate,

  $\text{A}\cup \text{B}$

The two events are mutually exclusive because it is impossible for an undergraduate to be both in business and in another field.

Apply addition rule for mutually exclusive events:

  $\begin{array}{l}P\left(\text{A}\cup \text{B}\right)=P\left(\text{A}\right)+P\left(\text{B}\right)\\ =0.20+0.15\\ =0.35\end{array}$

Thus,

Probability that the customer is currently an undergraduate is 0.35.

(c)

To determine

Probability for the customer is not an undergraduate business student.

Answer to Problem 40E

Probability that the customer is not an undergraduate business student is 0.80.

Explanation of Solution

Given information:

20% are undergraduate students in business.

15% are undergraduate students in other fields of study.

60% college graduates are currently employed.

Calculations:

According to the complement rule,

  $P\left({\text{A}}^c\right)=P\left(\text{not}\text{A}\right)=1-P\left(\text{A}\right)$

Let

A: Undergraduate students in business

B: Undergraduate students in other fields of study

C: College graduate who is currently employed

Note that

Probability for undergraduate business student

  $P\left(\text{B}\right)=20\%=0.20$

Apply complement rule:

  $\begin{array}{l}P\left({\text{B}}^c\right)=P\left(\text{not}\text{B}\right)=1-P\left(\text{B}\right)\\ =1-0.20\\ =0.80\end{array}$

Thus,

Probability that the customer is not an undergraduate business student is 0.80.