To find the probability that the selected family has no girls, we'll take the following steps:
1. Understand the total number of families: According to the given data:
[tex]\[
\begin{array}{|l|c|c|c|}
\hline
\text{Number of girls in a family} & 2 & 1 & 0 \\
\hline
\text{Number of families} & 45 & 75 & 180 \\
\hline
\end{array}
\][/tex]
The total number of families is the sum of these values:
[tex]\[
\text{Total number of families} = 45 + 75 + 180 = 300
\][/tex]
2. Identify the number of families with no girls: From the table, it is given that the number of families with 0 girls is 180.
3. Calculate the probability: Probability is defined as the ratio of the favorable outcomes to the total number of outcomes. In this context, the favorable outcomes are the families with no girls, and the total number of outcomes is the total number of families.
So, the probability [tex]\( P \)[/tex] that the selected family has no girls is:
[tex]\[
P(\text{no girls}) = \frac{\text{Number of families with no girls}}{\text{Total number of families}}
\][/tex]
Therefore:
[tex]\[
P(\text{no girls}) = \frac{180}{300}
\][/tex]
4. Simplify the fraction:
[tex]\[
\frac{180}{300} = \frac{18}{30} = \frac{3}{5} = 0.6
\][/tex]
Hence, the probability that the selected family has no girls is [tex]\( 0.6 \)[/tex] or 60%.
