2. An electronics store sells four brands of laptops. The least expensive 60% of

Question

2. An electronics store sells four brands of laptops. The least expensive 60% of sales. The other three brands, listed in order of increasing price, have the following percentages of sales: B2, 20%, B3 15% and B4, 5% The cheapest brand is also the most brand, Bl, accounts for 120 pts) y to need repairs during the warranty period. The probabilities of needing repairs while under warranty are: 0.09 for B1;0.06 for B2:0.04 for B3, and 0.02 (a) What is the probability that a laptop purchased from this store will need repairs during the warranty period? (b) Given that a laptop needs repairs during the warranty period, what is the probability that it is NOT the least expensive brand?

Explanation / Answer

Here we have

P(B1) = 0.60, P(B2) = 0.20, P(B3) = 0.15, P(B4) = 0.05

Let R shows the event that laptop need repair under warranty period. So

P(R|B1) = 0.09, P(R|B2) = 0.06, P(R|B3) = 0.04, P(R|B4) = 0.02

(A)

P(B1) = 0.60, P(B2) = 0.20, P(B3) = 0.15, P(B4) = 0.05

By the law of total probability, the required probability is

P(R) = P(R|B1) P(B1)+ P(R|B2)P(B2)+ P(R|B3)P(B3)+ P(R|B4)P(B4)= 0.09*0.60 + 0.06 * 0.20 + 0.04*0.15+ 0.02 * 0.05 = 0.073

(B)

P(not least expensive brand) = [ P(R|B2)P(B2)+ P(R|B3)P(B3)+ P(R|B4)P(B4) ] / P(R) = 0.019 / 0.073 = 0.2603

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