Suppose a computer chip manufacturer rejects 4% of the chips produced because th
ID: 3272491 • Letter: S
Question
Suppose a computer chip manufacturer rejects 4% 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 sixth chip they test is the first bad one they find. The probability is . b) Find the probability they find a bad one within the first 8 they examine. The probability is . c) Find the probability that the first bad chip they find will be the seventh one they test. The probability is . d) The first bad chip they find will be one of the first four they test. The probability is .Explanation / Answer
a) Probability that the sixth chip they test is the first bad one they find
= Probability that first five chips are not bad * Probability that the fourth chip is bad
= (1 - 0.04)5*0.04 = 0.033
Therefore 0.033 is the required probability here.
b) Probability that they find a bad one within the first 8 they examine
= 1- Probability that the first 8 are not bad
= 1 - ( 1 - 0.04)8
= 1 - 0.968
= 0.279
Therefore 0.279 is the required probability here.
c) Probability that the first bad chip is the seventh they test
= Probability that first 6 are not bad * Probability that the seventh one is bad
= 0.966*0.04
= 0.031
Therefore 0.031 is the required probability here.
c) The first bad chip they find will be one of the first four they test
= 1- Probability that there is no bad in first 4 they test
= 1 - 0.964
= 0.151
Therefore 0.151 is the required probability here.
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