.
Let me re-write the condition in a correct way, as it should be:
In a razor blade factory, machines A,B and C manufacture 25%, 35% and 40% of the total output respectively.
Of their respective outputs, 5%, 4% and 2% are defective razor blades. A razor blade is chosen at random and found to be defective.
Find the probability that it was manufactured by machine B
Solution
Let X = the total output amount of razor blades produced by all three machines A, B and C.
Then the machine A produces 0.25*X blade razors; of them, 0.05*0.25*X razors are defective.
The machine B produces 0.35*X blade razors; of them, 0.04*0.35*X razors are defective.
The machine C produces 0.40*X blade razors; of them, 0.02*0.40*X razors are defective.
The probability under the question is the ratio of the defective razors amount produced by the machine B, 0.04*0.35*X,
to the total amount of all defective razors produced by all 3 machines.
In other words, the probability under the question is this ratio
P =
=
= 0.4058 = 40.58% (approximately).
Solved.