Question

Preparing for the GMAT A company that offers courses to prepare students for the Graduate Management The admission Test (GMAT) has the following information about its customers: $20\%$ are currently undergraduate students in business; $15\%$ are undergraduate students in other fields of study; $60\%$ are

college graduates who are currently employed, and $5\%$ are college graduates who are not employed. Choose a customer at random.

(a) What’s the probability that the customer is currently an undergraduate? Which rule of probability did you use to find the answer?

(b) What’s the probability that the customer is not an undergraduate business student? Which rule of probability did you use to find the answer?

Short answer

Part (a) The likelihood is $0.15$

Part (b) The likelihood is $0.80$

Step-by-step solution

Part (a)  Step 1. Given Information

The company's tabular data shows that $20\%$ of its employees are currently undergraduate students studying business; 15% are undergraduate students studying other fields of study; $60\%$are college graduates who are currently employed; and $5\%$ are college graduates who are unemployed.

Part (a) Step 2. Concept Used

An event is a subset of an experiment's total number of outcomes. The ratio of the number of elements in an event to the number of total outcomes is the probability of that occurrence and the use of the complimentary rule.

Part (a)  Step 3. Calculation

$P(undergraduateinbu\sin ess)$ = $0.20$

$P(undergraduateinothersubjects)$ =$0.15$

$P(employedgraduates)$ = $0.60$

$P(unemployedgraduates)$ = $0.05$

Formula

$P(AorB)=P\left(A\right)+P\left(B\right)$

$P(Undergraduateinbu\sin essorotherfields)=P(Undergraduateinbu\sin ess)+P(Undergraduateinotherfields)=0.20+0.15=0.35(u\sin gformula)$

Part (b) Step 1. Calculation

$P(undergraduateinbu\sin ess)$ = $0.20$

$P(undergraduateinothersubjects)$ = $0.15$

$P(employedgraduates)$ = $0.60$

$P(unemployedgraduates)$ = $0.05$

Formula

$P\left(A^c\right)=1-P\left(A\right)$

Using complimentary formulas.

$P(Notundergraduatebu\sin ess)=1-P(Undergraduatebu\sin ess)=1-0.20=0.80$