Question

A survey shows that 70% of the indian like mangoes and 82% of them like apple if x% of indian like both apple and mango then?

Answer 1

Let mango liking people be in set M and apple liking people be in set A and total number of people be 100 i.e n(A∪M) = 100

(assuming there is no one who doesnot like any of these(apple or mango) i.e n(A∪M)' = 0)

Accordingly n(M) = 70 and n(A) = 82

using formula n(A∪M) = n(A) + n(M) - n(A∩M)

implies 100 = 70 + 82 - n(A∩M)

i.e both fruits are liked by 52% of people

Answer 2

Answer: The value of x% is 52%.

Step-by-step explanation:

Since we have given that

Percentage of Indian who like mangoes = 70%

Percentage of Indian who like apple = 82%

Total percentage of Indian = 100%

Let x% of Indian like both apple and mango.

so, Percentage of Indian who like both apple and mango is given by

$P(M\cap A)=P(M)+P(A)-P(M\cup B)\\\\P(M\cap A)=70\%+82\%-100\%\\\\P(M\cap A)=152\%-100\%\\\\P(M\cap A)=52\%$

Hence, the value of x% is 52%.