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

question 110

Multiple Choice

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)

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Definitions:

Solver

An optimization tool used in computational software that finds the maximum or minimum value of a function under given constraints.

Optimal Number

The most favorable quantity that leads to the best outcome or efficiency under given conditions.

Monthly Profit

The financial gain or loss calculated at the end of each month, resulting from revenue minus expenses.

Constraints

Restrictions or limitations on the decision-making process, which can include available resources, regulations, or specific conditions that must be met.