In the town of Maplewood a certain type of DVD player is sold at just two...

In the town of Maplewood a certain type of DVD player is sold at just two stores. 38% of the sales are from store A and the rest of the sales are from store B. 7% of the DVD players sold at store A are defective while 3% of the DVD players sold at store B are defective. If Kate receives one of these DVD players as a gift and finds that it is defective, what is the probability that it came from store A? Express your answer as a percentage rounded to the nearest hundredth.

Solutions

Expert Solution

P(store A) = 0.38

P(store B) = 1 - 0.38 = 0.62

P(defective | store A) = 0.07

P(defective | store B) = 0.03

P(defective) = P(defective | store A) * P(store A) + P(defective | store B) * P(store B)

= 0.07 * 0.38 + 0.03 * 0.62

= 0.0452

P(store A | defective) = P(defective | store A) * P(store A) / P(defective)

= 0.07 * 0.38 / 0.0452

= 0.5885

= 58.85% (ans)

orchestra answered 1 year ago

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