Answer to Question #335897 in Statistics and Probability for Karl

Question

If x represents the number of voys in a family of 7 children, find the probabbility and distribution

Answer 1

$X\sim Bin(n, p)$

$n=7, p=q=0.5.$

$$P(X=k)=\dbinom{7}{k}(0.5)^k(0.5)^{7-k}=\dfrac{\dbinom{7}{k}}{128}$$

$$\def\arraystretch{1.5} \begin{array}{c:c:c} x & p(x)\\ \hline 0 & 1/128\\ \hdashline 1 & 7/128\\ \hdashline 2 & 21/128\\ \hdashline 3 & 35/128\\ \hdashline 4 & 35/128\\ \hdashline 5 & 21/128\\ \hdashline 6 & 7/128\\ \hdashline 7 & 1/128\\ \hdashline \end{array}$$