The probability that in a family of 3 children, there will be at least one boy, is :

Question

Accepted Answer

To determine the probability that in a family of 3 children, there will be at least one boy, we need to consider all possible combinations of children and calculate the probability of each scenario.

1. **Total Possible Outcomes:**
   - Each child can either be a boy (B) or a girl (G).
   - Therefore, for 3 children, the total number of possible combinations is $2^3 = 8$.

2. **Outcomes with at least one boy:**
   - The combinations that include at least one boy are: 
     - BGG
     - GBG
     - GGB
     - BBG
     - BGB
     - GBB
     - BBB
   - There are 7 such combinations.

3. **Probability Calculation:**
   - The probability of having at least one boy is the number of favorable outcomes (at least one boy) divided by the total number of possible outcomes.
   - Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total possible outcomes}} = \frac{7}{8}$.

4. **Explanation of Options:**

- **Option 1: $\frac{1}{2}$**
     - This option suggests that the probability of having at least one boy is 50%. However, as calculated, there are 7 favorable outcomes out of 8, which is not equal to $\frac{1}{2}$.

- **Option 2: $\frac{1}{8}$**
     - This option implies that there is only one favorable outcome out of 8, which is incorrect. There are actually 7 favorable outcomes.

- **Option 3: $\frac{3}{4}$**
     - This option suggests that the probability is 75%. While this might seem plausible, it does not match the calculated probability of $\frac{7}{8}$.

- **Option 4: $\frac{7}{8}$**
     - This is the correct option as it accurately represents the probability of having at least one boy in a family of 3 children, based on the calculation above.

Therefore, the correct answer is Option 4: $\frac{7}{8}$. This option correctly reflects the probability of having at least one boy in a family of 3 children.