An assembler of electric fans uses motors from three sources. company a supplies 30%, company b supplies 40% and company c supplies the rest. the defect rates are as follows: 10% of the motors from company a are defective and 20% of the motors from company b are defective, and 15% of the motors from company c are defective. if a motor is found to be good, what is the probability it came from company b?

If a motor is found to be good, there is a 37.87% probability that it came from company B.

Step-by-step explanation:

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

For this problem, we have the following question:

What is the probability that the motors comes from company B, given that the motor is good?

P(B) is the probability of the motor coming from company B. Company B supplies 40%, so .

P(A/B) is the probability of the motor being good, given that it comes from company B. 20% of the motors from company B are, which means that 80% are good, so .

P(A) is the probability that the motor is good. Company A supplies 30% of the motors, of which 90% are good. Company B supplies 40% of the motors, of which 80% are good. Company C supplies the rest, that is 100%-(40%+30%) = 30%. Of which 85% are good. So:

Finally

If a motor is found to be good, there is a 37.87% probability that it came from company B.