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.

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles

answer: 88

step-by-step explanation: