An electronics store researched the TV sales in the last 6 months. The probabili

Question

An electronics store researched the TV sales in the last 6 months. The probability a customer would purchase the Brand 1 model TV was 70% while the rest of the customers purchased the Brand 2 model. Furthermore, 20% of the Brand 1 customers purchased an extended warranty while 40% of Brand 2 customers purchased an extended warranty. A customer is randomly selected from among all those who bought a TV from the store.

What is the probability that the selected customer purchased a Brand 1 model and an extended warranty? Round your answer to 2 decimal places.

Explanation / Answer

P(brand 1) = 0.7

P(brand 2) = 0.3

P(extended warranty | brand 1) = 0.2

P(extended warranty | brand 2) = 0.4

P(extended warranty) = P(extended warranty | brand 1) * P(brand 1) + P(extended warranty | brand 2) * P(brand 2)

                                   = 0.2 * 0.7 + 0.4 * 0.3

                                   = 0.26

P(brand 1 | extended warranty) = P(extended warranty | brand 1) * P(brand 1) / P(extended warranty)

                                                  = 0.2 * 0.7 / 0.26

                                                  = 0.54

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