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Question
Answer the following:
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?
Solution
Let X ≡ set of all students
A ≡ set of students who drink apple juice
B ≡ set of students who drink orange juice
We are given the following:
n(X) = 425, n(A) = 115, n(B) = 160 and n(A ∩ B) = 80
The Venn diagram is shown below :
The number of students who drink neither apple juice nor orange juice
= n[(A ∪ B)']
= n(X) – n(A ∪ B)
= 425 – (35 + 80 + 80)
= 425 – 195
= 230
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