# In class XI of a school,40% of the students study mathematics and 30% study biology.10% of the class study both mathematics and biology.If a student is selected at random from the class.Find the probabilities that he will be studying mathematics or biology.

$\begin{array}{1 1}(A)\;60\%\\(B)\;50\%\\(C)\;40\%\\(D)\;35\%\end{array}$

Toolbox:
• $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
Step 1:
Let M denote Mathematics,B denote Biology
$\therefore$ P(M)=0.40(40%)
$P(B)=0.30(30\%)$
$P(M \cap B)=0.10(10\%)$
Step 2:
$\therefore P$(M or B)=$P(M\cup B)$
$\Rightarrow P(M)+P(B)-P(M\cap B)$
$\Rightarrow 0.40+0.30-0.10$
$\Rightarrow 0.70-0.10$
$\Rightarrow 0.60=60\%$
Therefore,probability that he will be studying mathematics or biology is 60%
Hence (A) is the correct answer.