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???

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.

true

step-by-step explanation:

part a

in a city ice cream is mostly only bought when the temperature is very high as ice cream cools down our

so we can derive the conclusion that as the temperature increases the number of ice creams sold also increases

part b

y intercept is 5

slope is 2

happy to

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