100 families with two children were selected randomly and the following data were recorded :
`{:("No. of girls in family",2,1,0),("No. of families",12,80,8):}`
Calculate the probability of a family chosen at random having
no girl

Answer

To calculate the probability of a family chosen at random having no girls, follow these steps:

### Step 1: Understand the Data
We have data for 100 families with two children. The number of girls in each family can be 2, 1, or 0. The corresponding number of families for each case is given as:
- Families with 2 girls: 12
- Families with 1 girl: 80
- Families with 0 girls: 8

### Step 2: Identify Total Number of Families
The total number of families surveyed is 100.

### Step 3: Identify Favorable Outcomes
We need to find the number of families that have no girls. According to the data, the number of families with no girls is 8.

### Step 4: Calculate the Probability
The probability \( P \) of an event is calculated using the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the event is having no girls. Thus, we can substitute the values:
\[ P(\text{no girls}) = \frac{8}{100} \]

### Step 5: Simplify the Probability
Now, we simplify the fraction:
\[ P(\text{no girls}) = \frac{8}{100} = \frac{4}{50} = \frac{2}{25} \]

### Step 6: Convert to Decimal (Optional)
If needed, we can also express this probability in decimal form:
\[ P(\text{no girls}) = 0.08 \]

### Final Answer
The probability of a family chosen at random having no girls is \( \frac{2}{25} \) or 0.08.

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