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.

answer: $201

step-by-step explanation: to get the answer, you first get 3 nieces that he sold and multiply it by 67 and get $201, so he earned $201 selling his nieces.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1