A family with four children is randomly selected. Assume that births of boys and girls are equally likely. Construct a table showing the probability distribution for the events 4 girls, 3 girls, 2 girls, 1 girl, and 0 girls..
$\quad $ $\quad $$\quad $$\text {4 Child Family }$
$\begin{array}{l}
\begin{array} { l l c }
\hline { \text { Result } } && \text { Probability } \
\hline \
\
\
\
\
\hline \text { Total } & &
\end{array}
\end{array}$

A)
$\quad $ $\quad $$\quad $$\text {4 Child Family }$
$\begin{array}{l}
\begin{array} { l l c }
\hline { \text { Result } } && \text { Probability } \
\hline 4 \text { girls } & 0 \text { boys } & 1 / 16 \
3 \text { girls } & 1 \text { boy } & 4 / 16 \
2 \text { girls } & 2 \text { boys } & 6 / 16 \
1 \text { girl } & 3 \text { boys } & 4 / 16 \
0 \text { girls } & 4 \text { boys } & 1 / 16 \
\hline \text { Total } & & 1
\end{array}
\end{array}$

B) $\quad $ $\quad $$\quad $$\text {4 Child Family }$
$\begin{array}{l}
\begin{array} { l l c }
\hline { \text { Result } } && \text { Probability } \
\hline 4 \text { girls } & 0 \text { boys } & 1 \
3 \text { girls } & 1 \text { boy } & 1 \
2 \text { girls } & 2 \text { boys } & 1 \
1 \text { girl } & 3 \text { boys } & 1 \
0 \text { girls } & 4 \text { boys } & 1 \
\hline \text { Total } && 5
\end{array}
\end{array}$

C)
$\quad $ $\quad $$\quad $$\text {4 Child Family }$
$\begin{array}{l}
\begin{array} { l l c }
\hline { \text { Result } } && \text { Probability } \
\hline 4 \text { girls } & 0 \text { boys } & 1 / 5 \
3 \text { girls } & 1 \text { boy } & 1 / 5 \
2 \text { girls } & 2 \text { boys } & 1 / 5 \
1 \text { girl } & 3 \text { boys } & 1 / 5 \
0 \text { girls } & 4 \text { boys } & 1 / 5\
\hline \text { Total } && 1
\end{array}
\end{array}$

D)
$\quad $ $\quad $$\quad $$\text {4 Child Family }$
$\begin{array}{l}
\begin{array} { l l c }
\hline { \text { Result } } && \text { Probability } \
\hline4 \text { girls } & 0 \text { boys } & 1 \
3 \text { girls } & 1 \text { boy } & 4 \
2 \text { girls } & 2 \text { boys } & 6 \
1 \text { girl } & 3 \text { boys } & 4 \
0 \text { girls } & 4 \text { boys } & 1\
\hline \text { Total } && 16
\end{array}
\end{array}$

Question

A family with four children is randomly selected. Assume that births of boys and girls are equally likely. Construct a table showing the probability distribution for the events 4 girls, 3 girls, 2 girls, 1 girl, and 0 girls..   
$\quad $ $\quad $$\quad $$\text {4 Child Family }$
$\begin{array}{l}
\begin{array} { l l c } 
\hline { \text { Result } } && \text { Probability } \
\hline \
 \
 \
 \
 \
\hline \text { Total } & & 
\end{array}
\end{array}$

A)
  $\quad $ $\quad $$\quad $$\text {4 Child Family }$
$\begin{array}{l}
\begin{array} { l l c } 
\hline { \text { Result } } && \text { Probability } \
\hline 4 \text { girls } & 0 \text { boys } & 1 / 16 \
3 \text { girls } & 1 \text { boy } & 4 / 16 \
2 \text { girls } & 2 \text { boys } & 6 / 16 \
1 \text { girl } & 3 \text { boys } & 4 / 16 \
0 \text { girls } & 4 \text { boys } & 1 / 16 \
\hline \text { Total } & & 1
\end{array}
\end{array}$

B)  $\quad $ $\quad $$\quad $$\text {4 Child Family }$
$\begin{array}{l}
\begin{array} { l l c } 
\hline  { \text { Result } } && \text { Probability } \
\hline 4 \text { girls } & 0 \text { boys } & 1 \
3 \text { girls } & 1 \text { boy } & 1 \
2 \text { girls } & 2 \text { boys } & 1 \
1 \text { girl } & 3 \text { boys } & 1 \
0 \text { girls } & 4 \text { boys } & 1 \
\hline \text { Total } && 5
\end{array}
\end{array}$

C)
  $\quad $ $\quad $$\quad $$\text {4 Child Family }$
$\begin{array}{l}
\begin{array} { l l c } 
\hline  { \text { Result } } && \text { Probability } \
\hline 4 \text { girls } & 0 \text { boys } & 1 / 5 \
3 \text { girls } & 1 \text { boy } & 1 / 5 \
2 \text { girls } & 2 \text { boys } & 1 / 5 \
1 \text { girl } & 3 \text { boys } & 1 / 5 \
0 \text { girls } & 4 \text { boys } & 1 / 5\
\hline \text { Total } && 1
\end{array}
\end{array}$

D) 
  $\quad $ $\quad $$\quad $$\text {4 Child Family }$
$\begin{array}{l}
\begin{array} { l l c } 
\hline  { \text { Result } } && \text { Probability } \
\hline4 \text { girls } & 0 \text { boys } & 1 \
3 \text { girls } & 1 \text { boy } & 4 \
2 \text { girls } & 2 \text { boys } & 6 \
1 \text { girl } & 3 \text { boys } & 4 \
0 \text { girls } & 4 \text { boys } & 1\
\hline \text { Total } && 16
\end{array}
\end{array}$

Quizplus · Accepted Answer

The probabilities are calculated based on the binomial distribution formula, with each child having a 1/2 chance of being a girl or a boy. The total number of outcomes for 4 children is $2^4 = 16$. The probabilities in option A correctly reflect the number of ways each result can occur out of the 16 possible outcomes.

A Family with Four Children Is Randomly Selected \quad \quad

A Family with Four Children Is Randomly Selected $\quad$ $\quad$