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1. In a class, 30% of the students offered English, 20% offered Hindi and 10% offered both. If a student is selected at random, What is the probability that he has offered English or Hindi ?

A. $\frac{2}{5}$

B. $\frac{3}{5}$

C. $\frac{3}{4}$

D. $\frac{3}{10}$

Solution:

\begin{aligned} P (E) = \frac{30}{100} = \frac{3}{10}; \\ P (H) = \frac{20}{100} = \frac{1}{5} and \\ P (E \cap H) = \frac{10}{100} = \frac{1}{10} \end{aligned}

P (E or H) =

P (E \cup H)

= P(E) + P(H) -

P (E \cup H)

\begin{aligned} = (\frac{3}{10} + \frac{1}{5} - \frac{1}{10}) \\ = \frac{4}{10} \\ = \frac{2}{5} \end{aligned}

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