A couple plans to have children until they get a boy,but they agree that they will not have more than four children even if all are girls. Create a probability model for the number of children they will have.Assume that boys and girls are equally likely.
A) $$\begin{array} { l | c c c c }
\text { Children } & 1 & 2 & 3 & 4 \
\hline \text { P(Children) } & 0.5 & 0.25 & 0.125 & 0.125
\end{array}$$
B) $$\begin{array} { l | c c c c c }
\text { Children } & 1 & 2 & 3 & 4 & 5 \
\hline \text { P(Children) } & 0.5 & 0.25 & 0.125 & 0.0625 & 0.0625
\end{array}$$
C) $$\begin{array} { l | c c c }
\text { Children } & 1 & 2 & 3 \
\hline \mathrm { P } \text { (Children) } & 0.5 & 0.25 & 0.25
\end{array}$$
D) $$\begin{array} { l | c c c c }
\text { Children } & 1 & 2 & 3 & 4 \
\hline \mathrm { P } \text { (Children) } & 0.5 & 0.25 & 0.125 & 0.0625
\end{array}$$
E) $$\begin{array} { l | c c c c }
\text { Children } & 1 & 2 & 3 & 4 \
\hline \text { P(Children) } & 0.25 & 0.25 & 0.25 & 0.25
\end{array}$$

Question

A couple plans to have children until they get a boy,but they agree that they will not have more than four children even if all are girls. Create a probability model for the number of children they will have.Assume that boys and girls are equally likely.
A) $$\begin{array} { l | c c c c } 
\text { Children } & 1 & 2 & 3 & 4 \
\hline \text { P(Children) } & 0.5 & 0.25 & 0.125 & 0.125
\end{array}$$
B) $$\begin{array} { l | c c c c c } 
\text { Children } & 1 & 2 & 3 & 4 & 5 \
\hline \text { P(Children) } & 0.5 & 0.25 & 0.125 & 0.0625 & 0.0625
\end{array}$$
C) $$\begin{array} { l | c c c } 
\text { Children } & 1 & 2 & 3 \
\hline \mathrm { P } \text { (Children) } & 0.5 & 0.25 & 0.25
\end{array}$$
D) $$\begin{array} { l | c c c c } 
\text { Children } & 1 & 2 & 3 & 4 \
\hline \mathrm { P } \text { (Children) } & 0.5 & 0.25 & 0.125 & 0.0625
\end{array}$$
E) $$\begin{array} { l | c c c c } 
\text { Children } & 1 & 2 & 3 & 4 \
\hline \text { P(Children) } & 0.25 & 0.25 & 0.25 & 0.25
\end{array}$$

Quizplus · Accepted Answer

The probability of having a boy (and thus stopping) is 0.5 for the first child. If the first is a girl, the probability of having a boy as the second child is 0.5, but we must also account for the probability of the first being a girl (0.5), making it 0.5 * 0.5 = 0.25 for the second child. This pattern continues, with the probability halving each time. However, if they have three girls in a row (probability 0.125), they will stop at four children regardless, making the probability of having four children 0.125, not halving again because they stop regardless of the fourth child's gender.

A Couple Plans to Have Children Until They Get a Boy,but