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
\((c)\) How many people like only one of the following foods: nihari, biryani, or korma?
Let, \(N=\text{People like nihari}\; ;\)\(B=\text{People like biryani}\; ;\)\(\;K=\text{People like korma}\)
\(n(N)=40\)
\(n(B)=65\)
\(n(K)=50\)
\(n(N\cap B)=20\)
\(n(B\cap K)=35\)
\(n(N \cap K)=27\)
\(n(N\cap B \cap K)=12\)
\(n(N)\) \(\text{only}\) \(\ =\ \)\(n(N)-n(N\cap B)-n(N\cap K)+n(N\cap B\cap K\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ =40-20-27+12\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ =5\) people like nihari
\(n(B)\) \(\text{only}\) \(\ =\ \)\(n(B)-n(N\cap B)-n(B\cap K)+n(N\cap B\cap K\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ =65-20-35+12\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ =22\) people like Biryani
\(n(K)\) \(\text{only}\) \(\ =\ \)\(n(K)-n(N\cap K)-n(B\cap K)+n(N\cap B\cap K\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ =50-27-35+12\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ =0\) people like korma
\(\text{people who like only one of the three foods}\)\(\ =\ \)\(n(N)+n(B)+n(K)\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\(\ =\ \)\(5+22+0\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\(\ =\ \)\(27\)