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# In a hostel, 60% of the students read Hindi news paper, 40% read English news paper and 20% read both Hindi and English news papers. A student is selected at random. If she reads English news paper, find the probability that she reads Hindi news paper.

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## 1 Answer

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Toolbox:
• If A and B are independent events, $P(A\cap\;B)=P(A)\;P(B)$
• P ($\large\frac{A}{B}$) = $\large\frac{P (A \cap B)}{P(B)}$
Let H: the students who read Hindi newspapers, E: the students who read English newspapers.
Given $P (H) = 60\text{%} = 0.6, \; P(E) = 40\text{%} = 0.4, P (H \cap E) = 20\text{%} = 0.2$
(c) P (student reads Hindi paper if he/she reads an English paper)
P (Reads an Hindi paper / If he/she reads a English paper) = $\large\frac{P (E \cap H)}{P(E)} = \frac{0.2}{0.4}$$= 0.5$
answered Jun 19, 2013

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