Chapter 5.3, Problem 96E

To determine

To find: the probability that the person is a graduate student.

Answer to Problem 96E

The probability that the person is a graduate student is $0.25$ .

Explanation of Solution

Given:

40% mainly use a MAC.

67% are undergraduates.

23% of the graduates use mainly PC.

Concept used:

Definition conditional probability:

  $P\left(B|A\right)=\frac{P\left(A\text{ and}B\right)}{P\left(A\right)}$

Calculation:

According to question, combining the given information to obtain the following two-way table:

	Undergraduate	Graduate	Total
PC	37%	23%	60%
MAC	30%	10%	40%
Total	67%	33%	100%

Definition conditional probability:

  $P\left(B|A\right)=\frac{P\left(A\text{ and}B\right)}{P\left(A\right)}$

Evaluate using the two-way table, thus obtained:

  $\begin{array}{l}P\left(\text{Graduate}|\text{MAC}\right)=\frac{P\left(\text{Graduate and MAC}\right)}{P\left(\text{MAC}\right)}\\ =\frac{10\%}{40\%}=\frac{1}{4}=0.25\end{array}$

Hence,the probability that the person is a graduate student is $0.25$ .