Question

In a certain college, 25% of boys and 10% of girls are studying mathematics. The girls constitute 60% of the student body. If a student is selected at random and is found to be studying mathematics, the probability that the student is a girl is.

Answer 1

Hint: This question is of probability. So, we will first find probability by dividing favourable events by total number of events. So, in the given question we need to find favourable events. We need to assume the total number of students studying in a college is $100$. Then we will do the further calculation using the probability formula.

Complete step by step solution:
Let the number of students studying in the college be 100x.
Given, Girls constitute $60\%$
Boys constitute $40\%$
So, Number of girls $=60x$ and Number of boys $=40x$.
Percentage of boys studying mathematics $=25\%$
Number of boys studying mathematics $ = \dfrac{{25}}{{100}} \times 40x = 10x$ boys
Percentage of girls studying mathematics = $10\%$
Number of girls studying mathematics $ = \dfrac{{10}}{{100}} \times 60x = 6x$ girls
Total number of students studying mathematics (Girls + Boys) $= 10x + 6x = 16x$
If a student is selected at random and is found to be studying mathematics, the probability that the student is a girl $ = \dfrac{\text{number of girls studying mathematics}}{\text{total number of students studying mathematics}}$
$\Rightarrow$\[ \dfrac{{6x}}{{16x}} = \dfrac{3}{8}\]

$\therefore$ So, if a student is selected at random and is found to be studying mathematics, the probability that the student is a girl is \[\dfrac{3}{8}\].

Note:
Always remember, probability means possibility; this is the method to predict the chances of happening of an even. Probability used to predict how likely events to happen. In these types of questions, first we will find the total number of students studying mathematics including boys and girls both. Then we will find the probability that the student selected must be a girl studying mathematics.
Alternatively, this question can be done by assuming the total number of students as 100 as finding all percentage values in numbers and then comparing the ratio asked.