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

Answer:P=0.39Step-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 [tex]\begin{pmatrix}52\\4\end{pmatrix}[/tex]different ways .Taking 2 red cards can be done in [tex]\begin{pmatrix}26\\2\end{pmatrix}[/tex]different ways. Same applies to the black cards So, the required probability can be computed as [tex]P=\frac{\begin{pmatrix}26\\2\end{pmatrix}\begin{pmatrix}26\\2\end{pmatrix}}{\begin{pmatrix}52\\4\end{pmatrix}}[/tex][tex]{\begin{pmatrix}52\\4\end{pmatrix}}=\frac{52!}{4!48!}=270725[/tex][tex]{\begin{pmatrix}26\\2\end{pmatrix}}=\frac{26!}{2!24!}=325[/tex][tex]P=\frac{325x325}{270725}=0.39[/tex]