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

Answer

Expert–verified
Hide Steps
Answer

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 \(\boxed{0.143}\).

Steps

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 \(\boxed{0.143}\).

link_gpt