$\mathrm{P}\left(\mathrm{A}\right)=\frac{\mid \mathrm{A}\mid }{\mid \mathrm{\Omega }\mid }\backslash mathrm\; P\backslash left(\backslash mathrm\; A\backslash right)=\backslash frac\{\backslash left|\backslash mathrm\; A\backslash right|\}\{\backslash left|\backslash mathrm\backslash Omega\backslash right|\}$

Berechne $\mid \mathrm{A}\mid \backslash left|\backslash mathrm\; A\backslash right|$.

Es gibt $\left(\begin{array}{c}13\\ 6\end{array}\right)\backslash begin\{pmatrix\}13\backslash \backslash 6\backslash end\{pmatrix\}$ Möglichkeiten, 6 weiße Kugeln auszuwählen. Für jede dieser Möglichkeiten gibt es $\left(\begin{array}{c}16\\ 4\end{array}\right)\backslash begin\{pmatrix\}16\backslash \backslash 4\backslash end\{pmatrix\}$ Möglichkeiten, 4 rote Kugeln auszuwählen.

$\Rightarrow \mid \mathrm{A}\mid =\backslash Rightarrow\backslash left|\backslash mathrm\; A\backslash right|=$ $\left(\begin{array}{c}13\\ 6\end{array}\right)\backslash begin\{pmatrix\}13\backslash \backslash 6\backslash end\{pmatrix\}$ $\cdot \backslash cdot$ $\left(\begin{array}{c}16\\ 4\end{array}\right)\backslash begin\{pmatrix\}16\backslash \backslash 4\backslash end\{pmatrix\}$

Berechne nun $\mid \mathrm{\Omega }\mid \backslash left|\backslash mathrm\backslash Omega\backslash right|$.

Es gibt insgesamt $\left(\begin{array}{c}29\\ 10\end{array}\right)\backslash begin\{pmatrix\}29\backslash \backslash 10\backslash end\{pmatrix\}$ Möglichkeiten, um 10 Kugeln auszuwählen.

Berechne $\mathrm{P}(\mathrm{X}=6)\backslash mathrm\; P\backslash left(\backslash mathrm\; X=6\backslash right)$.

$\mathrm{P}(\mathrm{X}=6)=\frac{\left(\begin{array}{c}13\\ 6\end{array}\right)\cdot \left(\begin{array}{c}16\\ 4\end{array}\right)}{\left(\begin{array}{c}29\\ 10\end{array}\right)}=\backslash mathrm\; P\backslash left(\backslash mathrm\; X=6\backslash right)=\backslash frac\{\backslash begin\{pmatrix\}13\backslash \backslash 6\backslash end\{pmatrix\}\backslash cdot\backslash begin\{pmatrix\}16\backslash \backslash 4\backslash end\{pmatrix\}\}\{\backslash begin\{pmatrix\}29\backslash \backslash 10\backslash end\{pmatrix\}\}=$