A computer company manufactures chips in three facilities. Chips from facilities A, B, and C are defective with probabilities 0.004, 0.005, and 0.003 respectively. Assume that the proportions of chips from A, B, and C are 0.3, 0.3, and 0.4 respectively. (a) What is the probability that a randomly selected chip is defective? (b) If a randomly selected chip is found to be defective, what is the probability that it came from facility B? (c) If a randomly selected chip is found to be defective, what is the probability that it came from facility C?

a) 0.012

b) 0.036

c) 0.048

Step-by-step explanation:

a)

If we take a random sample of 1,000 chips, there must be

1,000*0.004 = 4 defective chips from facility A

1,000*0.005 = 5 defective chips from facility B

1,000*0.003 = 3 defective chips from facility C.

So, in a random sample of 1,000 chips there must be 12 defective chips, hence the probability that a randomly selected chip is defective is

12/1000 = 0.012

b)

The probability that a chip is defective and came from B is

P (the chip is defective) * P (the chip came from B) =

0.012*0.3 = 0.036

c)

The probability that a chip is defective and came from C is

P (the chip is defective) * P (the chip came from C) =

0.012*0.4 = 0.048