Answer: 0.20833
Step-by-step explanation:
This is a case of inverse probability.
We first determine the probability that an item is defective generally.
To do this we sum the possible options of having the item produced from the first machine and is defective or having the item produced by the second machine and is defective or having the item produced by the third machine and is defective.
Mathematically,this becomes :
(0.2 * 0.05) + (0.3 * 0.03) + (0.5 * 0.01)
0.01 + 0.009 + 0.005 = 0.024.
Probability an item is defective in general = 0.024
Probability a third machine produces a defective item = 0.5 * 0.01 = 0.005.
Hence, given that the item is defective, the probability that it was produced by the third machine becomes:
= (probability of the item being produced from the third machine and is defective) / (probability of the item being defective in general)
= 0.005/0.024
= 0.20833.
1/4= 0.25
2/4= 1/2 = 0.5
0.25 x 0.5 = 0.125
0.125 = 1/8
