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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salwanadeem salwanadeem · Answer 1 · 2020-02-19T07:03:42+01:00

Answer:

It is basically ³C₁ which is causing '3' to show up in the calculations.

Step-by-step explanation:

Basically, this question uses the binomial distribution formula for calculating the number of wafers that pass the test. The formula is:

P(X=x) = ⁿCₓ pˣ qⁿ⁻ˣ

where n = total number of wafers

x = number of wafers that pass the test

p = probability of passing the test

q = probability of failing the test.

For calculating P(X=1):

P(X=1) = ³C₁ (0.8)¹(0.2)²

P(X=1) = 3 (0.8)(0.2)²

So, here is where the '3' comes from! Its ³C₁ which means we are selecting 1 wafer that passes the test out of the 3 wafers.

Hope this answer helps.