In a family of 3 children the probability of having at least one boy is

Answer

To find the probability of having at least one boy in a family of three children, we can follow these steps:

### Step 1: Identify the total possible outcomes
When considering the gender of three children, each child can either be a boy (B) or a girl (G). Therefore, the total number of possible combinations for three children is calculated as follows:

\[ \text{Total outcomes} = 2^3 = 8 \]

The possible combinations are:
1. BBB (all boys)
2. BBG (two boys, one girl)
3. BGB (two boys, one girl)
4. GBB (two boys, one girl)
5. GGB (one boy, two girls)
6. GBG (one boy, two girls)
7. BGG (one boy, two girls)
8. GGG (all girls)

### Step 2: Identify the favorable outcomes
Next, we need to determine the number of outcomes that include at least one boy. The only combination that does not include a boy is GGG (all girls). Therefore, the favorable outcomes are all the other combinations:

- BBB
- BBG
- BGB
- GBB
- GGB
- GBG
- BGG

This gives us a total of 7 favorable outcomes.

### Step 3: Calculate the probability
The probability of an event is given by the formula:

\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we found:

\[ \text{Probability of at least one boy} = \frac{7}{8} \]

### Final Answer
Thus, the probability of having at least one boy in a family of three children is:

\[ \frac{7}{8} \]

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