A manufacturer produces a large number of microwaves. From past experience, the manufacturer knows that approximately 1.5% of all its microwaves are defective. Consumer Reports randomly selects 20 of these microwaves for testing. You want to determine the probability that no more than one of these microwaves is defective.

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- anonymous

What is the probability that at most two of the microwaves are defective?

- anonymous

It's just binomial distribution, no?

- anonymous

Yeah, but how would I get it with x<=2. I know how to do x=2, but not x<=2.

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- anonymous

\[
\Pr(X\leq 2) = \Pr(X=0, X=1, X=2) = \Pr(X =0) + \Pr(X = 1) +\Pr(X = 2)
\]

- anonymous

Ah, alright. Thanks. I get it now.

- anonymous

They're mutually exclusive events. They can't have both exactly 2 and exactly 1 defective microwave.

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