Question

From a standard deck of cards you draw 4 cards. Find the probability of drawing 2 red and 2 black cards.

Answer 1

P=0.39

Explanation:

We use the Hypergeometric distribution to find the probability

The normal deck of cards has 52 cards, 26 red and 26 black

Taking 4 cards out of the whole deck can be done (without replacement) in

`\begin{pmatrix}52\\4\end{pmatrix}`

different ways .

Taking 2 red cards can be done in

`\begin{pmatrix}26\\2\end{pmatrix}`

different ways. Same applies to the black cards

So, the required probability can be computed as

`P=\frac{\begin{pmatrix}26\\2\end{pmatrix}\begin{pmatrix}26\\2\end{pmatrix}}{\begin{pmatrix}52\\4\end{pmatrix}}`

`{\begin{pmatrix}52\\4\end{pmatrix}}=(52!)/(4!48!)=270725`

`{\begin{pmatrix}26\\2\end{pmatrix}}=(26!)/(2!24!)=325`

`P=(325x325)/(270725)=0.39`