Adepartment 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?

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