Problem7 The following table reports the proportions of microchips that a certai

Question

Problem7 The following table reports the proportions of microchips that a certain PC manufacturer purchases from seven suppliers. (adapted from [Mendenhall and Sincich 2016], exercise 3.56). It is known that the proportions of defective microchips produced by the seven suppliers are 0.001, 0.0003, 0.0007, 0.006, 0.0002,0.0002, and 0.001, respectively. If a single microchip failure is observed, what are the probabilities that each supplier is responsible? Instead assume that all suppliers produce defective microchips at the same rate of 0.0005. If a single microchip failure is observed, what are the probabilities that each supplier is responsible? a. b. Supplier Proportion S1 S2 S3 S4 S5 S6 S7 0.15 0.05 0.10 0.20 0.12 0.20 0.18

Explanation / Answer

a) P( FIrst supplier ) = 0.001/[0.001+0.0003+0.0007+0.006+0.0002+0.0002+0.001]=0.1063

P( S2) =  0.0003/[0.001+0.0003+0.0007+0.006+0.0002+0.0002+0.001]=0.03191

P(S3) = 0.0007/[0.001+0.0003+0.0007+0.006+0.0002+0.0002+0.001] =0.0744

P(s4) = 0.006/[0.001+0.0003+0.0007+0.006+0.0002+0.0002+0.001]=0.6382

P(s5)= 0.0002/[0.001+0.0003+0.0007+0.006+0.0002+0.0002+0.001]=0.0212

P(s6)=0.0002/[0.001+0.0003+0.0007+0.006+0.0002+0.0002+0.001]=0.0212

P(s7) = 0.001/[0.001+0.0003+0.0007+0.006+0.0002+0.0002+0.001] =0.1063

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