Question

Two technicians regularly make repairs when breakdowns occur on an automated production line. The first technician,...

Two technicians regularly make repairs when breakdowns occur on an automated production line. The first technician, who service 40% of the breakdowns, has 5% chance of making incomplete repair. The second technician, who services 60% of the breakdowns, has a 3% chance of making an incomplete repair. Given that there is a problem with the production line due to an incomplete repair, what is the probability that this initial repair was made by the first technician?

Math   Statistics-And-Probability   
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Answer #1

Given data:

1st technician service s1= 40%=0.4

chance of making incomplete repair of 1st technician i1=0.05

Probability for 1st technician make incomplete service P(1)= i1*s1=0.05*0.4 =0.02

2nd technician service s2= 60%=0.6

chance of making incomplete repair of 2nd technician i2=0.03

Probability for 2nd technician make incomplete service P(2)= i2*s2=0.03*0.6 =0.018

Probability for problem with the production line due to an incomplete repair P(1st & 2nd) =P(1)+P(2)= 0.018+0.02 = 0.038

Probability that problem in production line due to an incomplete repair that this initial repair was made by the first technician =P(1 | 1st & 2nd)

P(1 | 1st & 2nd) = P(1)/P(1st & 2nd) = 0.02/0.38

=0.5263

Probability that problem in production line due to an incomplete repair that this initial repair was made by the first technician is 0.5263

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