I am currently doing a self-study on Conditional Probability and faced the below question.
A manufacturing plant makes radios that each contains an integrated circuit (IC) supplied by three sources A, B and C. The probability that the IC in a radio came from one of the sources is 1/3, the same is true for all sources. ICs are known to be defective with probabilities 0.001, 0.003 and 0.002 for sources A, B and C respectively.
What is the probability any given radio will contain a defective IC?
Say, Rd - event of radio being defective
Given P(Rd|A) = 0.001, P(Rd|B) = 0.003 and P(Rd|C) = 0.002;
P(A) = P(B) = P(C) = 1/3
We have to find P(Rd) = probability of finding a defective IC in the radio
= P(Rd|A)*P(A) + P(Rd|B)*P(B) + P(Rd|C)*P(C)
P(Rd) = 1/3*(0.001 + 0.003 + 0.002) = 0.002
But the answer given is 0.005978. Not sure what's wrong with the approach I have taken. Any help is highly appreciated.