In a school there are 1000 students , out of which 430 girls . It is known that out of 430 , 10% of the girls study in class XII. What is the probability that a students chosen randomly studies in class XII ,given that the chosen students is a girl

Answer

To solve the problem step-by-step, we will calculate the required probability using the information given.

### Step 1: Determine the number of girls studying in class XII.
We know that there are 430 girls in total and 10% of these girls study in class XII.

\[ \text{Number of girls in class XII} = 10\% \text{ of } 430 = \frac{10}{100} \times 430 = 43 \]

### Step 2: Define the events.
Let:
- Event E: A student is chosen from class XII.
- Event F: A student is a girl.

### Step 3: Find the probability of event F.
The total number of girls is 430. Therefore, the probability of selecting a girl (event F) is:

\[ P(F) = \frac{\text{Number of girls}}{\text{Total number of students}} = \frac{430}{1000} \]

### Step 4: Find the probability of the intersection of events E and F.
The intersection of events E and F (i.e., choosing a student who is both in class XII and a girl) is the number of girls in class XII, which we calculated to be 43. Thus, the probability of selecting a girl from class XII is:

\[ P(E \cap F) = \frac{\text{Number of girls in class XII}}{\text{Total number of students}} = \frac{43}{1000} \]

### Step 5: Use the conditional probability formula.
We want to find the probability that a student chosen randomly studies in class XII given that the chosen student is a girl. This is represented as \( P(E | F) \) and can be calculated using the formula:

\[ P(E | F) = \frac{P(E \cap F)}{P(F)} \]

Substituting the values we found:

\[ P(E | F) = \frac{\frac{43}{1000}}{\frac{430}{1000}} = \frac{43}{430} = \frac{1}{10} \]

### Final Answer:
The probability that a student chosen randomly studies in class XII, given that the chosen student is a girl, is \( \frac{1}{10} \) or 0.1.

---