https://file.aiquickdraw.com/mathbot/file/1727057112546qz3grzaf.jpg

The problem asks to find the probability that a couple with four children has at least one girl, assuming boys and girls are equally likely.

### Step-by-Step Solution:

1. **Probability of Boy or Girl for Each Child:**
   - Since boys and girls are equally likely, the probability of a child being a girl is \( \frac{1}{2} \), and the probability of being a boy is also \( \frac{1}{2} \).

2. **Total Possible Outcomes:**
   - There are 4 children, and for each child, there are two possible outcomes (boy or girl). Therefore, the total number of possible outcomes is:
     \[
     2^4 = 16
     \]
     These are all the combinations of boys and girls in a family of four children.

3. **Complementary Event:**
   - It is easier to first find the probability of the complementary event: all four children are boys (i.e., no girls).
   - The probability of each child being a boy is \( \frac{1}{2} \), so the probability of all four children being boys is:
     \[
     P(\text{all boys}) = \left( \frac{1}{2} \right)^4 = \frac{1}{16}
     \]

4. **Probability of at Least One Girl:**
   - The probability of having at least one girl is the complement of the probability of having all boys. So:
     \[
     P(\text{at least one girl}) = 1 - P(\text{all boys}) = 1 - \frac{1}{16} = \frac{15}{16}
     \]

### Final Answer:
The probability that at least one of the four children is a girl is \( \frac{15}{16} \).

---

Do you have any questions or would you like more details?

Here are 5 related questions to deepen your understanding:
1. What is the probability of having exactly two girls in a family of four children?
2. How would the probability change if the likelihood of having a girl was not equal to the likelihood of having a boy?
3. What is the probability that all the children are either all boys or all girls?
4. How would the result change if the family had 5 children instead of 4?
5. Can you calculate the probability of having at least two girls among the four children?

**Tip:** When solving probability problems, the complement rule (finding the probability of the opposite event) often simplifies the calculation.

Find the probability that when a couple has four children, at least one of them is a girl. (Assume that boys and girls are equally likely.)

Find the probability that in a family with four children, at least one is a girl. This problem explores key probability concepts, using complementary events to calculate outcomes with equal likelihood for boys and girls.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation