In a survey among 100 people , it was found that 80% of those 100 people like the TV series F. R. I. E. N. D . S and 70% of all the 100 people like the tv series G. O. T . What is the minimum no of people who like both the tv series? Note that , some people may not like any of the two series ...
Answers
Given : In a survey among 100 people,
it was found that 80% of these 100 people like the TV series F.R.I.E.N.D.S and 70% of all the 100 people like the TV series G.O.T.
some people may not like any of the two series.
To Find : What is the minimum number of people who like both the TV series ,
Solution:
In a survey among 100 people,
hence n(Total ) = 100
80% of these 100 people like the TV series F.R.I.E.N.D.S
=> n(F) = 80
70% of all the 100 people like the TV series G.O.T.
=> n ( G) = 70
n(F∩G) = like both series
n ( none) = x does not like any series
0 ≤ x < (100 - 80) as 80 people like TV series F.R.I.E.N.D.S
=> 0 ≤ x ≤ 20
n (Total) = n(F) + n(G) - n(F∩G) + n(none)
=> 100 = 80 + 70 - n(F∩G) + x
=> n(F∩G) = 50 + x
n(F∩G) is minimum when x is minimum = 0
and maximum when x is maximum 20
Hence min n(F∩G) = 50 + 0 = 50
minimum number of people who like both the TV series are 50
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