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All electric circuit board failures can be classified into one of the following mutually exclusive and collectively exha...

All electric circuit board failures can be classified into one of the following mutually exclusive and collectively exhaustive categories: assembly defects (40%), electrical component defects (35%), and mechanical defects (25%). Suppose ten boards fail independently, and let the random variables X, Y, and Z denote the number of each type of defect among the boards respectively. What is P{X=8,Z=1|Y=1}?

math   Statistics-And-Probability   
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Answer #1

for conditional probability of X and Z if Y =1 are 0.4/0.65 and 0.25/0.65

P{X=8,Z=1|Y=1} =(9!/(8!*1!))*(0.4/0.65)8*(0.25/0.65)1 =0.071194 ~ 0.0712

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