3. At a factory, three robots (A, B and C) build devices, 20% of the devices...

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3. At a factory, three robots (A, B and C) build devices, 20% of the devices made by A are defective, 10% of the devices made by B are defective, and 5% of the devices made by machine C are defective. Each robot builds the same number of devices per day. Let F indicate a defective device (a) What is the probability P(F) that a given device produced in this factory is defective? (b) Given that a device is defective, what is the probability that it was produced by robot A? (c) Given that a device is not defective, what is the probability that it was produced by robot C?

math Statistics-And-Probability

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Answer 1

Answer #1

a)

P(F) =P(A)*P(F|A)+P(B)*P(F|B)+P(C)*P(F|C)=(1/3)*0.2+(1/3)*0.1+(1/3)*0.05=0.1167

b)

P(A|F) =P(A)*P(F|A)/P(F)=(1/3)*0.2/0.1167 =0.5714

c)

P(C|F^c)=P(C)*P( F^c|C)/P(F^c)=(1/3)*(1-0.05)/(1-0.1167)=0.3585

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Answer 2

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