13. In a survey report of 500 people, 225 people are suffering from T.B. while 260 people are suffering from cancer. There are 85 people suffering from both. Find the number of people who are suffering from neither of the both disease.
Answers
The total number of people = x
People suffering from T.B = y
people suffering from Cancer = x
People suffering from both disease = 85
Now ,
According to Question
x = 500
y = 225
z = 260
y∩z = 85
According to the survey report the number of people who are suffering from either of the both disease
y∩z= 225 + 260 - 85 = 400
Uy x ∪z = 500-400=100.
So the result is 100 , the number of people who are not suffering from both the disease are 100
Answer along with a step-by-step explanation:
Consider,
the set of all the people who participated in the survey be U
the set of people who suffer from T.B is A
the set of people who suffer from Cancer is B
Given,
n(U) = 500
n(A) = 225
n(B) = 260
n(A∩B) = 85
Therefore, the total number of people who suffer from either T.B or Cancer or both will be n(A∪B)
We know that,
n(A∪B) = n(A) + n(B) - n(A∩B)
Putting the value in the above equation, we get
n(A∪B) = 225 + 260 - 85 = 400
Therefore, the total number of people who do not suffer from neither of the both given diseases is:
n(U)- n(A∪B) = 500-400=100.
Therefore, there are 100 people, who took part in the survey neither suffering from T.B or Cancer.