Probability - Gravner-37

Question

A factory has three machines, M_1, M₂, and M₃, that produce items (say, light bulbs). It is impossible to tell which machine produced a particular item, but some are defective. Here are the known numbers:

machine	proportion of items made	prob. any made item is defective
M1	0.2	0.001
M2	0.3	0.002
M3	0.5	0.003

You pick an item, test it, and find it is defective. What is the probability that it was made by M_2?

Comments

answer is 0.26 denominator should 0.0023

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0.261

Answer 1

Probability of being defective:let D

Pr(Defective)=0.2x0.001+0.3x0.002+0.5x0.003=0.0024

P(M2/Defective)=P(Defective/M2)xP(M2)/P(Defective=0.002x 0.3/0.0024=0.25

Comments

i think denominator should be 0.0023