trigonometry

suppose a manufacterer of transistors believes that, on the average, one defective transistor occurs in every 100 transistors.

a. find the probability that a batch of 20 transistors has 2 defectives.

b. find the probability that a batch of 20 transistors has at most 2 defectives.

You can use something called the binomial probability function for these kinds of problems.
The function is this:
P(x) = (nCx)(p^x)[q^(n-x)]

For a:
n = 20
p = 1/100 = .01
q = 1 - p = 1 - .01 = .99

Substituting:
P(2) = (20C2)(.01^2)(.99^18) = (190)(.0001)(.8345) = .0159

For b:
n = 20
p = .01
q = .99
x = 0, 1, 2

Find P(0), P(1), and P(2). Add all values together for your probability.

I hope this helps.

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