In a hostel 60% of the students read Hindi news paper, 40% read English newspaper and 20% read both Hindi and English newspapers. A student is selected at random.

Answer

N/a

Explanation

Let `H=` group of students read Hind newspaper and `E=` group of students read English newspaper.
Now `n(S)=100` then `n(H)=60`
`n(E)=40` and `n(HnnE)=20`
`:.P(H)=(n(H))/(n(S))=60/100=3/5`
`P(E)=(n(E))/(n(S))=40/100=2/5`
and `P(HnnE)=(n(HnnE))/(n(S))=20/100=1/5`
(a) Required probability `=P` (she reads neither Hindi nor English newspapers)
`P(H'nnH')`
`=P(HuuE)'=1-P(HuuE)`
`=1-[P(H)+P(E)-P(HnnE)]`
`=1-(3/5+2/5-1/5)=1/5`
(b) Required probability `=P` (she reads Hindi newspaper then she reads English newspaper also)
`:.P(E/H)=(P(EnnH))/(P(H))=(1/5)/(3/5)=1/3`
(c) Required probabiity `=P` (she reads English newspaper then she reads Hindi newspaper also)
`:.P(H/E)=(P(HnnE))/(P(E))=(1/5)/(2/5)=1/2`