Question

Suppose a computer chip manufacturer rejects 5% of the chips produced because they fail presale testing. Assume the bad chips are independent. Complete parts a through d below. a) Find the probability that the fifth chip they test is the first bad one they find. The probability is (Type an integer or a decimal. Round to three decimal places as needed.) b) Find the probability they find a bad one within the first 7 they examine The probability is (Type an integer or a decimal. Round to three decimal places as needed.) c) Find the probability that the first bad chip they find will be the eighth one they test. The probability is (Type an integer or a decimal. Round to three decimal places as needed.) d) The first bad chip they find will be one of the first six they test. The probability is (Type an integer or a decimal. Round to three decimal places as needed.)

Answer 1

The probability that a chip is bad is, p=P(Bad chip) = 0.05 And, q =1-p =1-0.05 = 0.95 (a) The probability that the fifth chip they test is the first bad one they find is, (5h chip is the first bad) = (0.95)(0.95)(0.95)(0.95)(0.05) =(0.95)' (0.05) P = 0.040725313 z 0.0407 (b) The probability they find a bad one within the first 7 they examine is, P(bad one within the first 7 they examine) = 1- P(first 7 are not bad) =1-(0.95) = 0.301662704 z 0.3017

(c) The probability that the first bad chip they find will be the eighth one they test is, P(8* chip is the first bad)=(0.95)(0.95)(0.95)(0.95)(0.95)(0.95)(0.95)(0.05) = (0.95) (0.05) %3D = 0.034916865 z 0.0349 (d) The first bad chip they find will be one of the first six they test is, first bad chip they find find will be one =1-P(no bad chip in first 6 chips) of the first 6 they examine =1-(0.95) = 0.264908109 %3D z 0.2649