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].
