Question

63% americans eat cheese and 76% eat apple . find people who each both

Answer 1

Let A denotes, the set of Americans who like cheese and

B denotes those who like apples. Let the population of America be 100, then

n(A)=63andn(B)=76

Now, n(A∪B)=n(A)+n(B)−n(A∩B)

N(A∪B)=63+76−n(A∩B)

N(A∩B)=139−n(A∪B)

But n(A∪B)≤100

So, 139−n(A∪B)≥139−100

139−n(A∪B)≥39

n(A∩B)≥39…………(i)

Now,n(A∩B)≤n(A)andn(A∩B)≤n(B)

n(A∩B)≤63andn(A∩B)≤76

n(A∩B)≤63……………(ii)

From Eqs. (i) and (ii),

39≤n(A∩B)≤63

39≤x≤63