Suppose that the probability that a customer plans to make a purchase is 0.32. Suppose that the probability of responding to an advertisement given that the customer plans to make a purchase is 0.63 and that the probability of responding to an advertisement given that a person does not plan to make a purchase is 0.16. Given that a person responds to the advertisement, what is the probability that they plan to make a purchase?

0.6495

Step-by-step explanation:

This is question based on conditional probability

The probability that a customer plans to make a purchase = 0.32.

The probability that a customer plans not to make a purchase = 1 - 0.32

= 0.68

The probability of responding to an advertisement given that the customer plans to make a purchase = 0.63

The probability of responding to an advertisement given that a person does not plan to make a purchase = 0.16.

Given that a person responds to the advertisement, what is the probability that they plan to make a purchase is calculated as:

0.32 × 0.63/(0.32 × 0.63) + (0.16 × 0.68)

= 0.2016/ 0.2016 + 0.1088

= 0.2016/0.3104

= 0.6494845361

Approximately = 0.6495