«Banaketa binomial»: berrikuspenen arteko aldeak

\begin{alignarray}{rcl}

P(X = 3;4,1/6) & = & P[(2 \cap 2 \cap 2 \cap \overline{2}) \cup (2 \cap 2 \cap \overline{2}) \cap 2) \cup (2 \cap \overline{2}) \cap 2 \cap 2) \cup (\overline{2} \cap 2 \cap 2 \cap 2)]\\

& = & \BiggBig(\frac16 \times \frac16 \times \frac16 \times \frac56\BiggBig) + \BiggBig(\frac16 \times \frac16 \times \frac56 \times \frac16\BiggBig) + \BiggBig(\frac16 \times \frac56 \times \frac16 \times \frac16\BiggBig) + \BiggBig(\frac56 \times \frac16 \times \frac16 \times \frac16\BiggBig)\\

& = & 4 \times \BiggBig(\frac16 \times \frac16 \times \frac16 \times \frac56\BiggBig)=\frac{4!}{3!1!}\BiggBig(\frac{1}{6}\BiggBig)^3\BiggBig(\frac{5}{6}\BiggBig)^1=0.0154\\

\end{alignarray}