Preparing for the GMAT A company that offers courses to prepare students for the Graduate Management Admission Test (GMAT) has collected the following information about its customers: $20\%$are undergraduate students in business, $15\%$are undergraduate students in other fields of study, and $60\%$are college graduates who are currently employed. Choose a customer at random.

a. What must be the probability that the customer is a college graduate who is not currently employed? Why?

b. Find the probability that the customer is currently an undergraduate. Which probability rule did you use to find the answer?

c. Find the probability that the customer is not an undergraduate business student. Which probability rule did you use to find the answer?

We need find what must be the probability that the customer is a college graduate who is not currently employed.

By using complement rule,

$\mathrm{P}\left({\mathrm{A}}^{\mathrm{c}}\right)=\mathrm{P}\left(\overline{\mathrm{A}}\right)=1-\mathrm{P}\left(\mathrm{A}\right)$

Undergraduate Student in business are $20\%$

Undergraduate Student in other fields are $15\%$

Graduates who are currently employed are $60\%$

Let,

P(Graduates who are currently employed ) is P(A)

Therefore,

$$\begin{gathered} \mathrm{P}\left({\mathrm{A}}^{\mathrm{c}}\right)=1-\mathrm{P}\left(\mathrm{A}\right) \\ =1-0.60 \\ =0.40 \end{gathered}$$

Hence, $0.40$must be the probability that the customer is a college graduate who is not currently employed

We need to find probability that the customer is currently an undergraduate.

By using addition rule of mutually exclusive events :

$\mathrm{P}(\mathrm{A}\mathrm{U}\mathrm{B})=\mathrm{P}(\mathrm{A}\mathrm{or}\mathrm{B})=\mathrm{P}\left(\mathrm{A}\right)+\mathrm{P}\left(\mathrm{B}\right)$

Undergraduate Student in business are $20\%$

Undergraduate Student in other fields are$15\%$

Graduates who are currently employed are $60\%$

Let,

P(Undergraduate Student in business ) is P(A)

P(Undergraduate Student in other fields ) is P(B)

Therefore

P(currently an undergraduate ) is

$$\begin{gathered} \mathrm{P}(\mathrm{A}\mathrm{U}\mathrm{B})=\mathrm{P}\left(\mathrm{A}\right)+\mathrm{P}\left(\mathrm{B}\right) \\ =0.20+0.15 \\ =0.35 \end{gathered}$$

Hence, probability that the customer is currently an undergraduate is $0.35$

We need to find the probability that the customer is not an undergraduate business student.

By using complement rule,

$\mathrm{P}\left({\mathrm{A}}^{\mathrm{c}}\right)=\mathrm{P}\left(\overline{\mathrm{A}}\right)=1-\mathrm{P}\left(\mathrm{A}\right)$

Undergraduate Student in business are $20\%$

Undergraduate Student in other fields are $15\%$

Graduates who are currently employed are $60\%$

Let.

P(undergraduate business student ) is P(B)

So, P(not an undergraduate business student) is

$\mathrm{P}\left(\overline{\mathrm{B}}\right)=1-\mathrm{P}\left(\mathrm{B}\right)=1-0.20=0.80$

Hence the probability that the customer is not an undergraduate business student is $0.80$