A factory has three machines, M1, 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 M2?