Question

An Integrated Circuit (IC) chip is declared as "good" if it passes the quality acceptance test. Otherwise, the chip is declared as "bad". A mechanical machine produces two IC chips in pairs. Tests show that the first chip is good with probability 3/5. When the first chip is good, the probability that the second chip is good is 4/5. When the first chip is bad, the probability that the second chip is good is 2/5. a) What is the probability that both chips are good? b) What is the probability that both chips are bad? c) What is the probability that exactly one chip is good?

Answer 1

a) The probability of both chips being good = 0.48

b) The probability of both chips being bad = 0.24

c) The probability of one chip being good = 0.60

Explanation:

Probability of first chip being good = 3/5 = 0.60

Probability of second chip being good = 4/5 = 0.80

Probability of first chip being bad = 0.40 or 2/5 (1 - 3/5)

Probability of second chip being good if the first is bad = 2/5 = 0.4

Therefore, the probability of it being bad = 0.60 (1 - 0.40)

For both chips to be good, the probability = 0.60 * 0.80 = 0.48

For both chips to be bad, the probability = 0.60 * 0.40 = 0.24