Chapter 9.1, Problem 21E

(a)

To determine

All the elements to form the sample space of the set $S=\left\{gggg,gggb,ggbg,\mathrm{...}\right\}$.

(b)

To determine

To calculate: The values of the table and sketch the graph of the probability distribution, where the random variable $x$ is number of girl child. The table provided is

$\begin{array}{cccccc}x& 0& 1& 2& 3& 4\\ P\left(x\right)& & & & & \end{array}$.

(c)

To determine

To calculate: The probability that at least one children is a boy using the table provided in part b, the table provided is

$\begin{array}{cccccc}x& 0& 1& 2& 3& 4\\ P\left(x\right)& \frac{1}{16}& \frac{4}{16}& \frac{6}{16}& \frac{4}{16}& \frac{1}{16}\end{array}$