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Mathematics, 19.02.2020 03:52 deflox74

In a semiconductor manufacturing process, three wafers from a lot are tested. Each wafer is classified as pass or fail. Assume that the probability that a wafer passes the test is 0.8 and that wafers are independent.

Determine the probability mass function of the number of wafers from a lot that pass the test.

P[X=0]= (0.2)^3 This is because the probability that a wafer fails is 1-(0.8)=0.2
So for 3 wafers = (0.2)^3
P[X=1]= (0.2)^2*(0.8) This is because the probability that two wafers fail is (0.2)(0.2) or (0.2)^2 and the probability that 1 wafer passes is (0.8)

We can multiply these to find the probability because each event is independent

but the answer in the book has 3(0.2)^2*(0.8) Where does the 3 come from???

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