Question

A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 50% of the cameras sold have been of the basic model. Of those buying the basic model, 34% purchase an extended warranty, whereas 47% of all deluxe purchasers do so. If you learn that a randomly selected purchaser has an extended warranty, how likely is it that he or she has a basic model

Answer 1

0.4198 = 41.98% probability that he or she has a basic model

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Extended warranty

Event B: Basic model

Probability of extended warranty:

34% of 50%(basic model)

47% of 100 - 50 = 50%(deluxe model). So

`P(A) = 0.34*0.5 + 0.47*0.5 = 0.405`

Intersection of events A and B:

34% of 50%(basic model with extended warranty). So

`P(A \cap B) = 0.34*0.5 = 0.17`

How likely is it that he or she has a basic model

`P(B|A) = (P(A \cap B))/(P(A)) = (0.17)/(0.405) = 0.4198`

0.4198 = 41.98% probability that he or she has a basic model