Question 13: A survey was conducted in which 130 people were asked about their favourite foods. The survey results showed the following information:
* 40 people said they like nihari
* 65 people said they liked biryani
* 50 people said they liked korma
* 20 people said they liked nihari and biryani
* 35 people said they liked biryani and korma
* 27 people said they liked nihari and korma
* 12 people said they liked all three foods nihari, biryani, and korma
\((a)\) At least how many people like nihari, biryani, or korma?
Solution:
Let, \(N=\text{People like nihari}\; ;\)\(B=\text{People like biryani}\; ;\)\(\;K=\text{People like korma}\)
\(n(N \cup B \cup K)=?\)
\(n(N)=40\)
\(n(B)=65\)
\(n(K)=50\)
\(n(N\cap B)=20\)
\(n(B\cap K)=35\)
\(n(N \cap K)=27\)
\(n(N\cap B \cap K)=12\)
We know that
\(n(N\cup B\cup K)=\ \)\(n(N)+n(B)+n(K)\ \)\(−\ n(N\cap B)−n(B\cap K)\ \)\(−\ \)\(n(N\cap K)+n(N\cap B\cap K)\)
\(n(N \cup B \cup K)=\ \)\(40+65+50\ \)\(−\ 20−35\ \)\(−\ \)\(27+12\)
\(n(N \cup B \cup K)=85\)
\(\boxed{85 \text{ people like nihari, biryani, or korma}}\)