Question

A company that manufactures and sells consumer video cameras sells two versions of their popular hard disk​ camera, a basic camera for ​$750​, and a deluxe version for ​$1450. About 35​% of customers select the basic camera. Of​ those, 20​% purchase the extended warranty for an additional ​$200. Of the people who buy the deluxe​ version, 40​% purchase the extended warranty. What is the percentage of customers who buy an extened warranty?

Answer 1

The percentage of customers who buy an extended warranty is 33%.

Explanation:

In this problem, we have these following percentages.

35% of the customers select the basic camera.

This also means that:

65% of the customers select the deluxe version. (Since you can buy only two versions of the hard disk camera and the sum of the percentages is 100%).

20% of those who select the basic camera also purchase the extended warranty.

40% of those who select the deluxe version also purchase the extended warranty.

What is the percentage of customers who buy an extened warranty?

`P = P_(1) + P_(2)`

`P_(1)` is the percentage of those who buy the basic version with the extended warranty. So it is 20% of 35%. So

`P_(1) = 0.20*0.35 = 0.07`

`P_(2)` is the percentage of those who buy the deluxe version with the extended warranty. So it is 40% of 65%. So

`P_(2) = 0.40*0.65 = 0.26`

`P = P_(1) + P_(2) = 0.07 + 0.26 = 0.33`

The percentage of customers who buy an extended warranty is 33%.