Question

in a survey of 80 patients in a hospital, 20 were listed as taking apple juice, 30 as taking orange juice and 15 were listed as preferring both apple as well as orange juice. find how many patients were taking neither apple juice nor orange juice?

Answer 1

15 people as 20+30+15=65 .... so total minus 65

Answer 2

Answer:

Number of patient were taking neither Apple Juice nor Orange juice is 45.

Step-by-step explanation:

Given:

Number of patients in hospital = 80

Number of patient taking Apple Juice = 20

Number of patient taking Orange Juice = 30

Number of patient taking both Apple Juice and Orange Juice = 15

To find: Number of patient were taking neither Apple Juice nor Orange juice.

Let A represent set of patient taking Apple Juice and O represent set of patient taking Orange Juice. u represent Universal set of all patients in hospital.

Then we have,

n(U) = 80

n(A) = 20

n(O) = 30

n(A∩O) = 15

Consider,

n(A∪O) = n(A) + n(O) - n(A∩O) = 20 + 30 - 15 = 35

Number of Patients taking at least one type of Juice = 35

Number of patient were taking neither Apple Juice nor Orange juice

=n(U) - n(A∪O)

= 80 - 35

= 45

Therefore, Number of patient were taking neither Apple Juice nor Orange juice is 45.