TITLE: What is the probability of choosing $3$ objects from an event?
QUESTION [0 upvotes]: The probability that a randomly chosen person eats fruits is $0.22$, and the probability that he's healthy is $0.4$. The probability that he eats fruits AND is healthy is $0.12$. Suppose you choose $3$ people at random. What is the probability that all three people eat fruits?  
Clearly, those are two mutually inclusive events, which are dependent. Here's what I did, which I believe is wrong.  
$0.22^3=0.011$
This seems way too simple, and I don't know what I'm missing.

REPLY [1 votes]: This seems way too simple, and I don't know what I'm missing.

You are missing nothing.   It is that simple.   The question just contains a lot of distracting details; the main task was finding what you needed and ignoring the rest.
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