Chapter 13.5, Problem 39E

To determine

To explain: If a person who asked questions is more likely to buy something than the average person.

Answer to Problem 39E

Yes, it is true that if a person who asked questions is more likely to buy something.

Explanation of Solution

Given information:

A sample survey of 500 people recorded that number of people who bought something are 250, number of people who asked questions and bought something are 120 and number of people who asked questions and did not buy anything are 30.

Formula used:

Probability of an event E is $P\left(\text{E}\right)=\frac{\text{number of outcome}}{\text{total number of outcome}}$ .

Given an event Q, the conditional probability of event A is $P\left(A|Q\right)=\frac{P\left(A\text{ and Q}\right)}{P\left(Q\right)}$ where $P\left(Q\right)\ne 0$ .

Calculation:

Consider the provided information that the sample survey of 500 people recorded that number of people who bought something are 250, number of people who asked questions and bought something are 120 and number of people who asked questions and did not buy anything are 30.

Let A be an event that person bought something and B be an event that person asked questions.

Recall that probability of an event E is $P\left(\text{E}\right)=\frac{\text{number of outcome}}{\text{total number of outcome}}$ .

Probability that person asked questions,

  $P\left(B\right)=\frac{150}{500}$

Probability that person bought something and person asked questions,

  $P\left(A\text{ and B}\right)=\frac{120}{500}$

Recall that given an event Q, the conditional probability of event A is $P\left(A|Q\right)=\frac{P\left(A\text{ and Q}\right)}{P\left(Q\right)}$ where $P\left(Q\right)\ne 0$ .

The probability that person bought something provided that person asked questions.

  $\begin{array}{c}P\left(A|B\right)=\frac{\frac{120}{500}}{\frac{150}{500}}\\ =\frac{12}{15}\\ =\frac{4}{5}\end{array}$

Therefore, 4 out of 5 persons asked questions and bought something.

Yes, it is true that if a person who asked questions is more likely to buy something.