Problem 6-15 Items produced by a parts supplier have the following percentages o

Question

Problem 6-15 Items produced by a parts supplier have the following percentages of items satisfactory in the respective categories: Dimension 94% Weight 96% Texture 95% Assume an item's status is independent from category to category. Let Ds and Du denote the events that the next item produced will be satisfactory or unsatisfactory in dimension, with Ws and Wu serving analogously to denote the events for weight and Ts and Tu for texture. The probability of the elementary event DsWsTs equals Pr[Ds and Ws and Ts]. Use the multiplication law to find the probability for each fthe following elementary events:

Explanation / Answer

Here we have to use the simple multiplicative rule is:

P(DsWsTs) = P(Ds)P(Ws)P(Ts) = 0.94*0.96*0.95 = 0.85728

P(DuWuTu) = P(Du)P(Wu)P(Tu) = 0.06*0.04*0.05 = 0.00012

P(DsWuTu) = P(Ds)P(Wu)P(Tu) = 0.94*0.04*0.05 = 0.00188

P(DuWsTu) = P(Du)P(Ws)P(Tu) = 0.06*0.96*0.05 = 0.00288

P(DuWsTs) = P(Du)P(Ws)P(Ts) = 0.06*0.96*0.95 = 0.05472

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