A family has exactly 4 children. Assuming that each child born is equally likely to be boy or girl,then what is the sample space that the event to heaving exactly one girl child ?

Answer

To find the sample space for the event of having exactly one girl child in a family with four children, we can follow these steps:

### Step 1: Define the total number of children
We know that the family has exactly 4 children.

### Step 2: Identify the gender of each child
Each child can either be a boy (B) or a girl (G).

### Step 3: Determine the event of interest
We are interested in the event where there is exactly one girl among the four children.

### Step 4: List all possible combinations
To have exactly one girl, we can place the girl in any one of the four positions (first, second, third, or fourth). The remaining positions will be filled with boys.

Here are the combinations:
1. Girl in the first position: GBBB
2. Girl in the second position: BGBB
3. Girl in the third position: BBGB
4. Girl in the fourth position: BBGB

### Step 5: Write the sample space
The sample space for the event of having exactly one girl child is:
- {GBBB, BGBB, BBGB, BBBG}

### Final Answer
The sample space for the event of having exactly one girl child is {GBBB, BGBB, BBGB, BBBG}.

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