Question

A survey asked 281 people what alternative transportation modes they use. The results are below. 153 walk 137 use the bus 137 ride a bicycle 85 walk and use the bus 67 walk and ride a bicycle 90 ride the bus and ride a bicycle 49 said they use all three modes of transportation How many people only ride the bus?

Answer 1

11 people only ride the bus

Explanation:

Let A, B and C represents the event of walking, taking bus and taking a bicycle respectively.

According to the question,

n(A) = 153,

n(B) = 137,

n(C) = 137,

n(A∩B) = 85,

n(A∩C) = 67,

n(B∩C) = 90,

n(A ∩ B ∩ C) = 49,

Hence, the number of people who only ride the bus = n(B) - n(A∩B) - n(B∩C) + n(A ∩ B ∩ C)

= 137 - 85 - 90 + 49

= 11