There are three sections A,B and C in a class .Every section has some boy and some girl students in it .Probability of a girl being selected when one student is selected randomly from section A is `(2)/(5)` , that from section B is `(4)/(9)` and that from section C is `(5)/(9)`.
If the ratio of total number of students in sections A,B and C is 10 : 12 : 9 ,then what is the probability of a girl being selected when one student is selected randomly from the students from all the three sections together ?

Options

A. A)`(14)/(31)`
B. B)`(11)/(23)`
C. C)`(13)/(31)`
D. D)`(43)/(93)`

Answer

To solve the problem, we need to find the probability of selecting a girl when a student is chosen randomly from all three sections combined. Here’s how we can approach the solution step by step:

### Step 1: Define the Ratios
The ratio of total students in sections A, B, and C is given as 10:12:9. We can denote the total number of students in sections A, B, and C as:
- Let the total number of students in section A = 10x
- Let the total number of students in section B = 12x
- Let the total number of students in section C = 9x