Working on probability, just have a question that I can't get and I was looking for an explanation.
Suppose there is a box with 42 marbles. 20 white, 10 black, 6 red, 6 green. You choose 4 marbles at random without replacement. What is the chance you picked 2 white and 2 black? Also, what is the chance you get one of each color?
Best Answer
There are $\displaystyle \binom {42}4$ ways of choosing $4$ marbles from $42$ without replacement. But to choose $2$ whites from $20$, $2$ blacks from $10$ and $0$ from the others you have $\displaystyle \binom {20}2 \displaystyle \binom {10}2\displaystyle \binom {6}0 \displaystyle \binom {6}0$. And the probability is $$\text P(\{\ 2 \ Whites, \ 2\ Blacks\ \})\cfrac {\displaystyle \binom {20}2 \displaystyle \binom {10}2\displaystyle \binom {6}0 \displaystyle \binom {6}0 }{\displaystyle \binom {42}4} $$ways
I think you can do the "one of each color" now.
This is a hypergeometric distribution, see this example.