Question

In a survey of 425 students in a school, it was found that 115 drink apple juice, 160 drink orange juice, and 80 drink both apple as well as orange juice. How many drinks neither apple juice nor orange juice?

Answer 1

Let A = set of students who drink apple juice

B = set of students who drink orange juice

X = set of all students

∴ n(X) = 425, n(A) = 115, n(B) = 160, n(A ∩ B) = 80

No. of students who neither drink apple juice
nor orange juice = n(A' ∩ B') = n(A ∪ B)'

= n(X) – n(A ∪ B)

= 425 – [n(A) + n(B) – n(A ∩ B)]

= 425 – (115 + 160 – 80)

= 230