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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 Hindi news paper, find the probability that she reads English news paper.

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  • 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 $P (H) = 60\text{%} = 0.6, \; P(E) = 40\text{%} = 0.4, P (H \cap E) = 20\text{%} = 0.2$
(b) P (that a students reads an English paper if he/she reads a Hindi paper)
P ($\large\frac{A}{B}$) = $\large\frac{P (A \cap B)}{P(B)}$
P (Reads an English paper / If he/she reads a Hindi paper) = $\large\frac{P (E \cap H)}{P(H)} = \frac{0.2}{0.6} $$= 0.33$


answered Jun 19, 2013 by balaji.thirumalai

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