In a hostel, 60% of the students read Hindi newspaper 40% read English newspaper and 20% read both read both Hindi and English newspapers. A student is selected at random
Find the probability that he/she reads neither Hindi nor English newspapers.

If he/she reads Hindi newspaper, find teh probability that she reads English newspaper.

IF he/she reads Hindi newspaper, find the probability that she reads English newspaper.

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Solution

Let H: set of students reading Hindi newspaper and E: set of students reading English newspaper.
Let $n (S) = 100 t h e n, n (H) = 60 n (E) = 40 a n d n (H \cap E) = 20 ∴ P (H) = \frac{n (H)}{n (S H} = \frac{60}{100} = \frac{3}{5}, P (E) = \frac{n (E)}{n (s)} = \frac{40}{100} = \frac{2}{5} a n d P (H \cap E) = \frac{n (H \cap E)}{n (S)} == \frac{20}{100} = \frac{1}{5}$
Required probability = P (student reads neither Hindi
nor English newspaper)
$= P (H^{'} \cap E^{'}) = P (H \cup E)^{'} = 1 - P (H \cup E) = 1 - [P (H) + P (E) - P (H \cap E)] = 1 - [\frac{3}{5} + \frac{2}{5} - \frac{1}{5}] = \frac{1}{5}$

Let H: set of students reading Hindi newspaper and E: set of students reading English newspaper.
Let $n (S) = 100 t h e n, n (H) = 60 n (E) = 40 a n d n (H \cap E) = 20 ∴ P (H) = \frac{n (H)}{n (S H} = \frac{60}{100} = \frac{3}{5}, P (E) = \frac{n (E)}{n (s)} = \frac{40}{100} = \frac{2}{5} a n d P (H \cap E) = \frac{n (H \cap E)}{n (S)} == \frac{20}{100} = \frac{1}{5}$
Required probability = P(a randomly chosen student reads English newspaper, if he/she reads HIndi newspaper)
$∴ P (\frac{E}{H}) = \frac{P (E \cap H)}{P (H)} = \frac{\frac{1}{5}}{\frac{3}{5}} = \frac{1}{3}$

Let H: set of students reading Hindi newspaper and E: set of students reading English newspaper.
Let $n (S) = 100 t h e n, n (H) = 60 n (E) = 40 a n d n (H \cap E) = 20 ∴ P (H) = \frac{n (H)}{n (S H} = \frac{60}{100} = \frac{3}{5}, P (E) = \frac{n (E)}{n (s)} = \frac{40}{100} = \frac{2}{5} a n d P (H \cap E) = \frac{n (H \cap E)}{n (S)} == \frac{20}{100} = \frac{1}{5}$
Required probability = P (student reads Hindi newspaper when it is given that reads English newspaper)
$∴ P (\frac{H}{E}) = \frac{P (H \cap E)}{P (E)} = \frac{\frac{1}{5}}{\frac{2}{5}} = \frac{1}{2}$

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Similar questions

In a hostel, 60% of the students read Hindi newspaper 40% read English newspaper and 20% read both read both Hindi and English newspapers. A student is selected at random
If he/she reads Hindi newspaper, find teh probability that she reads English newspaper.

In a hostel, 60% of the students read Hindi newspaper 40% read English newspaper and 20% read both read both Hindi and English newspapers. A student is selected at random
IF he/she reads Hindi newspaper, find the probability that she reads English newspaper.

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