Answer:
0.76
Step-by-step explanation:
To find the probability that an employee has at least one child given that they are married, we can use the concept of conditional probability.
Given information:
- Total number of employees = 100
- Number of married employees = 75
- Number of employees with at least one child = 57
- Number of married employees without children = 33
1. Find the probability that an employee has at least one child and is married:
\[ P(\text{Married and at least one child}) = \frac{57}{100} \]
2. Find the probability that an employee is married:
\[ P(\text{Married}) = \frac{75}{100} \]
3. Find the probability that an employee is married and has at least one child:
\[ P(\text{Married and at least one child}) = \frac{57}{100} \]
4. Find the probability that an employee has at least one child given that they are married using the formula for conditional probability:
\[ P(\text{At least one child | Married}) = \frac{P(\text{Married and at least one child})}{P(\text{Married})} \]
5. Substitute the values:
\[ P(\text{At least one child | Married}) = \frac{57/100}{75/100} \]
\[ P(\text{At least one child | Married}) = \frac{57}{75} = \frac{19}{25} \]
Therefore, the probability that an employee has at least one child given that they are married is \( \frac{19}{25} \) or 0.76.
