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?

Answer:a) 0.012b) 0.036c) 0.048Step-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