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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?
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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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