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?

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

Tundexi Tundexi · Answer 2 · 2022-03-11T11:30:47+01:00

The Probability Refrigerator purchased from store to lasts more than 15 years is 0.1475 and the Probability that the Refrigeratorit was made by Company B is B: 0.3389.

Probability Refrigerator purchased from store lasts more than 15 years:

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

Probability that the Refrigeratorit was made by Company B:

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

= P (B/15) = [P(B).P(15/B)] / [P15]

= [(0.25)(0.20)] / 0.1475

= 0.05 / 0.1475

= 0.3389