Question

To help plan the number of meals to be prepared in a college cafeteria, a survey was conducted with the following data: 130 students ate breakfast (B), 180 students ate lunch (L), 275 students ate dinner (D), 68 students ate breakfast and lunch, 112 students ate breakfast and dinner, 90 students ate lunch and dinner, and 58 students ate all three meals. How many of the students (a) ate at least one meal in the cafeteria? (b) ate exactly one meal in the cafeteria? (c) ate only dinner in the cafeteria? (d) ate exactly two meals in the cafeteria?

Answer 1

a). 181

b). 219

c). 131

d). 96

Explanation:

As per data given,

n(B) = 8

n(L) = 80

n(D) = 131

n(B∩L) = 10

n(L∩D) = 32

n(B∩D) = 54

n(B∩L∩D) = 58

a). Students who ate at least one meal in the cafeteria.

Since n(B∪L∪D) = n(B) + n(L) + n(D) - n(B∩L) - n(L∩D) - n(B∩D) + n(B∩L∩D)

= 8 + 80 + 131 - 10 - 32 - 54 + 58

= 181

b). Students who ate exactly one meal = n(B)+n(L)+n(D)

= 8 + 80 + 131

= 219

c). Students who ate only dinner n(D) = 131

d). Students who ate exactly two meals in the cafeteria = n(B∩L) + n(L∩D) + n(B∩D)

= 10 + 32 + 54

= 96