Question:
In class, 30% of the students offered mathematics 20% offered chemistry and 10% offered both. If a student is selected at random, find the probability that he has offered mathematics or chemistry.
Solution:
Given: Math students = 30%
Chemistry Students $=20 \%$
Math \& Chemistry both $=10 \%$
To Find: P(Math or Chemistry)
Now, $\mathrm{P}$ (Math) $=30 \%=\frac{30}{100}=0.30$
$\mathrm{P}($ Chemistry $)=20 \%=\frac{20}{100}=0.20$
$\mathrm{P}($ Math $\cap$ Chemistry $)=10 \%=\frac{10}{100}=0.10$
We know that,
$P(A \cup B)=P(A)+P(B)-P(A \cap B)$
Therefore,
$P($ Math $\cup$ Chemistry $)=0.30+0.20-0.10=0.40$
Hence, number of students studying math or chemistry are 40%