Question

company that manufactures video cameras pro- duces a basic model and a deluxe model. over the past year, 40% of the cameras sold have been the basic model. of those buying the basic model, 30% purchase an ex- tended warranty, whereas 50% of all purchasers of the deluxe model buy an extended warranty. if you learn that a randomly selected purchaser bought an extended war- ranty, what is the probability that he or she has a basic model?

Answer 1

The probability that he or she has a basic model is 28.57%.

How to calculate the probability?

This situation required conditional probability using this formula

P(B|E) = P(B∩E) ÷ P(E)

P(B|E) is the probability of he or she only have basic model, if he or she bought extended warranty.

P(B∩E) is the probability of he or she have basic model and extended warranty.

P(E) is the probability of he or she bought extended warranty.

First, calculate P(B∩E)

P(B∩E) = 0.4 × 0.3

= 0.12

Next, calculate P(E)

P(E) = 0.4 × 0.3 + 0.6 × 0.5

= 0.12 + 0.3

= 0.42

Then, put P(B∩E) and P(E) to formula

P(B|E) = 0.12 ÷ 0.42

= 0.2857 or 28.57%

Thus, there is a 28.57% chance that he or she has a basic model.

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