In a family of three children, find the probability of having at least two boys.

Answer

To solve the problem of finding the probability of having at least two boys in a family of three children, we can follow these steps:

### Step 1: Determine the Sample Space
First, we need to identify all the possible outcomes when having three children. Each child can either be a boy (B) or a girl (G). Therefore, the sample space consists of the following combinations:

1. BBB (3 boys)
2. BBG (2 boys, 1 girl)
3. BGB (2 boys, 1 girl)
4. BGG (1 boy, 2 girls)
5. GBB (2 boys, 1 girl)
6. GBG (1 boy, 2 girls)
7. GGB (1 boy, 2 girls)
8. GGG (3 girls)

Thus, the total number of outcomes in the sample space is 8.

### Step 2: Identify Favorable Outcomes
Next, we need to find the outcomes that satisfy the condition of having at least two boys. The favorable outcomes are:

1. BBB (3 boys)
2. BBG (2 boys, 1 girl)
3. BGB (2 boys, 1 girl)
4. GBB (2 boys, 1 girl)

So, there are 4 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:

\[ \text{Probability} = \frac{4}{8} = \frac{1}{2} \]

### Final Answer
Therefore, the probability of having at least two boys in a family of three children is \(\frac{1}{2}\).

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