Question

How do you find the probability of drawing a card (there are 4 of that kind in the deck) in a 60 card deck. You draw 7 cards in the beginning.

Answer 1

depends on what your extra seven cards are

Answer 2

and what 7 cards are drawn later.

Answer 3

I don't think you get it. You have a 60 card deck. There is 4 of one kind in it and I want to know what the probability of drawing one of those cards in the beginning. The thing is you get to draw 7 cards in the beginning not just 1. We don't really care about the other 56 cards those can be anything and we don't care what happens after we draw those initial 7 cards.

Answer 4

Do you want to know what the probability of drawing exactly one of the 4 in the 7, or at least one of the 4? Since it does make a difference...

Answer 5

Probability of drawing exactly 1 of the 4:

\[\left(\begin{matrix}4 \\ 1\end{matrix}\right) \left(\begin{matrix}56 \\ 6\end{matrix}\right) \over \left(\begin{matrix}60 \\ 7\end{matrix}\right)\]

Probability of drawing at least one of the 4:

\[1 - {\left(\begin{matrix}4 \\ 0\end{matrix}\right) \left(\begin{matrix}56 \\ 7\end{matrix}\right) \over \left(\begin{matrix}60 \\ 7\end{matrix}\right)}\]