Sells 4 brands of DVD players. Least expensive, B1 accounts for 40%of sales. The

Question

Sells 4 brands of DVD players. Least expensive, B1 accounts for 40%of sales. The other brands(order of price) have following: B2=30%,B3=20%, B4=10%. Respective probabilities of needing repair duringwarranty are .10 for B1, 0.05 for B2, .03 for B3, and .02 for B4.Randomly selected purchaser has a DVD player that needs repairunder warranty. What are the four conditional probabilities ofbeing brand Bi, i=1,2,3,4?

I tried P(B1/Repair) but got the wrong answer, so I am doing itwrong and would like some help.

Explanation / Answer

Total probability of repair = .40 * .10 + .30 * .05 + .20 * .03 +.10 * .02 = .063 Probability of a DVD being a B1 in need of repair = .40 * .10 =.04 Probability of a DVD being a B2 in need of repair = .30 * .05 =.015 Probability of a DVD being a B3 in need of repair = .20 * .03 =.006 Probability of a DVD being a B4 in need of repair = .10 * .02 =.002 Given DVD needs repair under warrenty, Prob B1 = .04/.063 = .6349 Prob B2 = .015/.063 = .2381 Prob B3 = .006/.063 = .0952 Prob B4 = .002/.063 = .0317

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