Micro processing chips are randomly sampled one by one from a large population,
ID: 3271474 • Letter: M
Question
Micro processing chips are randomly sampled one by one from a large population, and tested to determine if they are acceptable for a certain application. Ninety-five (95) percent of the chips in the population are acceptable
a) What is the probability that the first chip chosen is acceptable?
b) What is the probability that the first chip is unacceptable, and the second is acceptable?
c) Let X represent the number of chips tested up to and including the first acceptable chip. Find P(X=3).
d) Find the probability mass function of X.
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Explanation / Answer
a) P(First chip chosen is acceptable) = 0.95
b) P(First chip is unacceptable and second is acceptable) = 0.05*0.95 = 0.0475
c) P(X = 3) = 0.05*0.05*0.95 = 0.052*0.95 = 0.002375
d) Probability mass function:
P(X = x) = (0.05)x-1 (0.95)