Problem

The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable $x$ represents the number of girls among 8 children. Complete parts (a) through (d) below. Click the icon to view the table. a. Find the probability of getting exactly 6 girls in 8 births. 0.117 (Type an integer or a decimal. Do not round.) b. Find the probability of getting 6 or more girls in 8 births. 0.109375 (Type an integer or a decimal. Do not round.) Probability Distribution for $\mathrm{x}$ \begin{tabular}{c|c} \hline $\begin{array}{c}\text { Number of } \\ \text { Girls } \mathbf{x}\end{array}$ & $\mathbf{P}(\mathbf{x})$ \\ \hline 0 & 0.005 \\ \hline 1 & 0.021 \\ \hline 2 & 0.117 \\ \hline 3 & 0.211 \\ \hline 4 & 0.292 \\ \hline 5 & 0.211 \\ \hline 6 & 0.117 \\ \hline 7 & 0.021 \\ \hline 8 & 0.005 \\ \hline \end{tabular} Print Done

Solution

Step 1 :The problem provides a table that describes the probability distribution for the number of girls in 8 births. The random variable $x$ represents the number of girls.

Step 2 :Part (a) asks for the probability of getting exactly 6 girls in 8 births. From the table, we can see that the probability of getting exactly 6 girls is 0.117.

Step 3 :Part (b) asks for the probability of getting 6 or more girls in 8 births. This means we need to add up the probabilities of getting 6, 7, and 8 girls.

Step 4 :From the table, the probability of getting 6 girls is 0.117, the probability of getting 7 girls is 0.021, and the probability of getting 8 girls is 0.005.

Step 5 :Adding these probabilities together gives us a total probability of 0.143 for getting 6 or more girls in 8 births.

Step 6 :Final Answer: The probability of getting exactly 6 girls in 8 births is \(\boxed{0.117}\). The probability of getting 6 or more girls in 8 births is \(\boxed{0.143}\).

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Source: https://solvelyapp.com/problems/16686/

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