A department store sells refrigerators from four manufacturers: 40% from Company A, 25% from Company B, 15% from Company C, and the rest come from Company D. Suppose 10% of the refrigerators from Company A, 20% from Company B, 5% from Company C, and 25% from company D last more than 15 years.

(a) What is the probability that a refrigerator purchased from this department store lasts more than 15 years?

(b) If a refrigerator purchased from this department store lasts more than 15 years, what is the probability that it was made by Company B?

Question

Jacoby Fisher

Business

15 August, 15:34

A department store sells refrigerators from four manufacturers: 40% from Company A, 25% from Company B, 15% from Company C, and the rest come from Company D. Suppose 10% of the refrigerators from Company A, 20% from Company B, 5% from Company C, and 25% from company D last more than 15 years.

(a) What is the probability that a refrigerator purchased from this department store lasts more than 15 years?

(b) If a refrigerator purchased from this department store lasts more than 15 years, what is the probability that it was made by Company B?

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Answers (1)

Know the Answer?

Grimes · Answer 1

A: 0.1475, B: 0.3389

Explanation:

a. Probability Refrigerator purchased from store lasts more than 15 years:

Prob (refrigerator purchase from A) and Prob (refrigerator from A life > 15 years) + ... Prob (refrigerator purchase from D) and Prob (refrigerator from D life >15 years)

(0.40x0.1) + (0.25x0.20) + (0.15x0.05) + (0.20x0.25) = 0.04+0.05+0.0075+0.05 = 0.1475

b. Refrigerator last > 15 years given, Probability it is from B:

[ Prob (B Purchase). Prob (life > 15, given from B) ] / Prob (Life > 15)

P (B/15) = [P (B). P (15/B) ] / [P15] {Bayes Theorum}

= [ (0.25) (0.20) ] / 0.1475 = 0.05 / 0.1475

= 0.3389