Suppose there is a drawer that contains 16 black socks and 4

Suppose there is a drawer that contains 16 black socks and 4 white socks. You draw 6 socks WITH REPLACEMENT.

What is the probability that you draw 4 black and 2 white socks?

Solution

Hi! Note that if you draw exactly 2 white socks, then what other choice do the other 4 socks have? Nothing. The other 4 needs to be black.

That\'s why

P(2 white) = P(4 black and 2 white).

This doesn\'t work if you have more than 2 colors, that is.

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In this case, it just seems that we didn\'t consider the balck, because you are thinking it is just a binomial distribution. It actually is--but it is strictly a multinomial distribution with only 2 variables, hence, a binomial.