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.

Question

anonymous · Answer

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

anonymous · Answer

It's just binomial distribution, no?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Ah, alright. Thanks. I get it now.

anonymous · Answer

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