A group of 78 people watch NDTV, Times Now and Republic. Out of these news channels, 36watch NDTV, 48 watch Times Now and 32 watches Republic. 14 people watch both NDTV and Times Now,20 people watch both Times Now and Republic, and 12 people watch both Republic and NDTV. Find the ratio of the number of people who watch only Times Now to the number of people who watch only Republic.
Solution
$$P\left(A\ U\ B\ U\ C\right)=P\left(A\right)+P\left(B\right)+P\left(C\right)-\left\{P\left(A∩B\right)+P\left(B∩C\right)+P\left(C∩A\right)\right\}+P\left(A∩B∩C\right)$$
Let the no. of people who watch all three be x
78= 36+48+32-(14+20+12)+x
or x= 8
No. of people who watch times now only = 48 - (14+20)+8 = 22
No. of people who watch republic only = 32 - (20+12) + 8 = 8
Ratio = 22/8 = 11:4
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