Search any question & find its solution
Question:
Answered & Verified by Expert
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 probability that he will be studying Mathematics or Biology.
Solution:
1616 Upvotes
Verified Answer
Probability that students study mathematics $=\frac{40}{100}=0.4$ or $P(M)=0.4$
Probability that students study Biology $=\frac{30}{100}=0.3$ or $P(B)=0.3$
Probability that students study bothmathematics and Biology $=\frac{10}{100}=0.1$
$P(M \cap B)=0.1$
We have to find the probability that a student studies mathematics or Biology means we have to find $P(M \cup B)$
Now,
$\begin{aligned}
&P(M \text { or } B)=P(M)+P(B)-P(M \cap B) \\
&=0.4+0.3-0.1=0.6
\end{aligned}$
Probability that students study Biology $=\frac{30}{100}=0.3$ or $P(B)=0.3$
Probability that students study bothmathematics and Biology $=\frac{10}{100}=0.1$
$P(M \cap B)=0.1$
We have to find the probability that a student studies mathematics or Biology means we have to find $P(M \cup B)$
Now,
$\begin{aligned}
&P(M \text { or } B)=P(M)+P(B)-P(M \cap B) \\
&=0.4+0.3-0.1=0.6
\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.