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Question

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


Solution

Total number of students $$= 1000$$
Total number of girls $$= 430$$

Girls studying in class $$XII = 10 \% \text{ of } 430$$

                                            $$ \\ = \cfrac{10}{100} \times 430$$

                                            $$ \\ = 43$$

We need to find the probability that a student chosen randomly studies in class $$XII$$, given that the chosen student is a girl.
$$A$$ : Student is in class $$XII$$
$$B$$ : Studenet is a girl

Therefore,
$$P{\left( A | B \right)}$$ $$= \cfrac{P{\left( A \cap B \right)}}{P{\left( B \right)}} \\ = \cfrac{\text{No. of girls studying in class XII}}{\text{Number of girls}} \\ = \cfrac{43}{430} = 0.1$$

Mathematics

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