Assuming that for a husband-wife couple the chance of their child being a boy or a girl are the same, the probability of their two children being a boy and a girl is

Options

A. `1/4`
B. 1
C. `1/2`
D. `1/8`

Answer

To solve the problem of finding the probability of a husband-wife couple having two children, one being a boy and the other being a girl, we can follow these steps:

### Step 1: Determine the Probability of Each Child's Gender
Since the problem states that the probability of having a boy (B) or a girl (G) is the same, we have:
- Probability of Boy (P(B)) = 1/2
- Probability of Girl (P(G)) = 1/2

### Step 2: Identify the Possible Outcomes for Two Children
When a couple has two children, the possible combinations of genders can be represented as:
1. Boy and Boy (BB)
2. Boy and Girl (BG)
3. Girl and Boy (GB)
4. Girl and Girl (GG)

### Step 3: Calculate the Probability of Each Combination
Each of these combinations can occur with the following probabilities:
- P(BB) = P(B) * P(B) = (1/2) * (1/2) = 1/4
- P(BG) = P(B) * P(G) = (1/2) * (1/2) = 1/4
- P(GB) = P(G) * P(B) = (1/2) * (1/2) = 1/4
- P(GG) = P(G) * P(G) = (1/2) * (1/2) = 1/4

### Step 4: Combine the Probabilities for One Boy and One Girl
The scenarios where there is one boy and one girl are:
- Boy and Girl (BG)
- Girl and Boy (GB)

To find the total probability of having one boy and one girl, we add the probabilities of these two scenarios:
- P(BG) + P(GB) = (1/4) + (1/4) = 1/2

### Final Answer
Thus, the probability of the couple having two children, one being a boy and the other being a girl, is **1/2**.

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