There are two children in a family. Find the probability that at most one boy is there in the family.

Explanation

To solve the problem of finding the probability that there is at most one boy in a family with two children, we can follow these steps:

### Step 1: Identify the Sample Space
First, we need to identify all possible outcomes for the genders of the two children. Each child can either be a boy (B) or a girl (G). Thus, the possible combinations for two children are:
1. Boy - Boy (BB)
2. Boy - Girl (BG)
3. Girl - Boy (GB)
4. Girl - Girl (GG)

So, the sample space (S) is:
\[ S = \{ BB, BG, GB, GG \} \]

### Step 2: Count the Total Outcomes
From the sample space, we can see that there are a total of 4 outcomes.

### Step 3: Define the Favorable Outcomes
Next, we need to find the outcomes that satisfy the condition of having at most one boy. The cases that meet this condition are:
1. Boy - Girl (BG)
2. Girl - Boy (GB)
3. Girl - Girl (GG)

Thus, the favorable outcomes (F) are:
\[ F = \{ BG, GB, GG \} \]

### Step 4: Count the Favorable Outcomes
From the favorable outcomes, we can see that there are 3 outcomes that satisfy the condition of having at most one boy.

### Step 5: Calculate the Probability
The probability (P) of an event is given by the formula:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we found:
\[ P(\text{at most one boy}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{4} \]

### Final Answer
The probability that there is at most one boy in the family is:
\[ \frac{3}{4} \]

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