A family has two children. If one of them is boy, then the probability that other is also a boy, is

Options

A. `1/2`
B. `1/4`
C. `1/3`
D. `1/5`

Answer

To solve the problem, we need to find the probability that if one child is a boy, the other child is also a boy. Let's break this down step by step.

### Step 1: Identify the Sample Space
When a family has two children, the possible combinations of children can be represented as:
1. Boy and Boy (BB)
2. Boy and Girl (BG)
3. Girl and Boy (GB)
4. Girl and Girl (GG)

However, since we know that at least one child is a boy, we can eliminate the combination where both children are girls (GG). Thus, the remaining combinations are:
- Boy and Boy (BB)
- Boy and Girl (BG)
- Girl and Boy (GB)

### Step 2: Count the Favorable Outcomes
From the remaining combinations, we need to find the cases where both children are boys. The only combination that satisfies this condition is:
- Boy and Boy (BB)

So, there is 1 favorable outcome (BB).

### Step 3: Count the Total Outcomes
The total number of outcomes that we have after eliminating GG is 3:
1. BB
2. BG
3. GB

### Step 4: Calculate the Probability
The probability that the other child is also a boy given that one child is a boy can be calculated using the formula:
\[ P(\text{Other is Boy | One is Boy}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} \]
Substituting the values we found:
\[ P(\text{Other is Boy | One is Boy}) = \frac{1}{3} \]

### Conclusion
Thus, the probability that the other child is also a boy, given that one of them is a boy, is \( \frac{1}{3} \).

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