binompdf (6,.4,2)

binompdf (6,.4,2) ?

$\text{binompdf (6,.4,2) } ?\\ \boxed{~ \text{binompdf } (n,\ p,\ x) =\binom{n}{x} \cdot p^x\cdot q^{n-x} ~}\\ $

$\begin{array}{rcl} p&=& 0.4\\\\ q&=&(1-p) \\ &=& 1-0.4\\ &=&0.6\\\\ n &=& 6 \\ x &=& 2 \\\\ \text{binompdf } (6,.4,2)=\\ P(X=2) &=& \binom{6}{2}\cdot 0.4^2\cdot0.6^4 \\ &=& \frac62\cdot\frac51\cdot 0.4^2\cdot0.6^4 \\ &=& 15\cdot 0.4^2\cdot0.6^4 \\ &=& 15\cdot 0.16\cdot0.6^4 \\ &=& 15\cdot 0.16\cdot0.1296 \\ &=&0.31104\\ &=& 31.104\ \% \end{array}$

0.31104