Answer:
15
Step-by-step explanation:
Let n(T) denotes total surveys done i.e. n(T)=140
Let n(A) be the no. of responses to positively to effectiveness i.e. n(A)=71
Let n(B) be the no. of side effects i.e.n(B) =60
Let n(C) be the no. of responses to cost i.e. n(C)= 65
33 responded positively to both effectiveness and side effects
So, n(A∩B)=33
31 to effectiveness and cost
n(A∩C)=31
28 to side effects and cost
n(B∩C)=28
21 to none of the items
So, n(A∪B∪C)=140-21 = 119
we are supposed to find ow many responded positively to all three i.e. n(A∩B∩C)
Formula:
n(A∪B∪C)=n(A)+n(B)+n(C)-n(A∩B)-n(A∩C)-n(B∩C)+ n(A∪B∪C)
119=71+60+65-33-31-28+ n(A∪B∪C)
119=104+ n(A∪B∪C)
119-104= n(A∪B∪C)
15= n(A∪B∪C)
Hence 15 responded positively to all three
