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In class, 30% of the students offered mathematics 20% offered chemistry and 10% offered both.

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%

 

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