Question

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

Answer 1

Answer:

P=0.39

Step-by-step 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

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

${\begin{pmatrix}52\\4\end{pmatrix}}=\frac{52!}{4!48!}=270725$

${\begin{pmatrix}26\\2\end{pmatrix}}=\frac{26!}{2!24!}=325$

$P=\frac{325x325}{270725}=0.39$