Question

In class $XI$ of a school $40\%$ of the students study Mathematics and $30\%$ study Biology. $10\%$ of the class studies both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.

Answer 1

Here in this problem we are given with the probability of students studying Mathematics, Biology and both. With the help of formulae $P(A \cup B) = P\left( A \right) + P\left( B \right) - P\left( {A \cap B} \right)$ we can find the probability of students studying either Mathematics or Biology.

Complete step-by-step answer:
Given: Probability that a student will study mathematics is $P\left( M \right) = \dfrac{{40}}{{100}} = \dfrac{2}{5}$
Probability that a student will study biology is $P\left( B \right) = \dfrac{{300}}{{100}} = \dfrac{3}{{10}}$
Probability that a student will study both biology and mathematics is$P\left( {M \cap B} \right) = \dfrac{{10}}{{100}} = \dfrac{1}{{10}}$
We have to find probability of they study mathematics or biology $P\left( {M \cup B} \right) = P\left( M \right) + P\left( B \right) - P\left( {M \cap B} \right)$
By substituting the values, we get –
$P\left( {M \cup B} \right) = \dfrac{2}{5} + \dfrac{3}{{10}} - \dfrac{1}{{10}} = 0.6 = \dfrac{6}{{10}}$
So, the probability that a student will study biology or mathematics is $\dfrac{6}{{10}}$.

Note: Here in these types of questions students usually make mistakes by considering the values incorrectly. While simplifying the solution one must take care about calculations.