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Q 27/30

Three hundred families with 2 children each were selected randomly, and the following data were recorded:

\begin{tabular}{|l|c|c|c|}
\hline
Number of girls in a family & 2 & 1 & 0 \\
\hline
Number of families & 45 & 75 & 180 \\
\hline
\end{tabular}

Out of these families, one family is selected at random. What is the probability that the selected family has no girls?



Answer :

GinnyAnswer
Sure, let's solve this problem step-by-step:

1. Understand the given data:
- There are a total of 300 families.
- The distribution of families based on the number of girls is given as follows:

| Number of girls in a family | Number of families |
|-----------------------------|--------------------|
| 2 | 45 |
| 1 | 75 |
| 0 | 180 |

2. Identify what we need to find:
- We need to find the probability that a randomly selected family has no girls.

3. Recall the basic probability formula:
Probability of an event [tex]\( P(E) \)[/tex] is given by:
[tex]\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \][/tex]

4. Determine the number of favorable outcomes:
- The number of families with no girls is 180.

5. Determine the total number of possible outcomes:
- The total number of families is 300.

6. Calculate the probability:
[tex]\[ P(\text{no girls}) = \frac{\text{Number of families with no girls}}{\text{Total number of families}} = \frac{180}{300} \][/tex]

7. Simplify the fraction:
[tex]\[ \frac{180}{300} = 0.6 \][/tex]

Therefore, the probability that a randomly selected family has no girls is [tex]\(0.6\)[/tex].