Question

In a student community, 30% of the students own a car and 50% of the students who own a car also own a bicycle. Also, 60% of the student community own a bicycle. Furthermore 25% of students who own a bicycle, also own a two-wheeler. Car owners do not own two-wheelers. Finally, 30% of the students own a two-wheeler. What is the probability that a randomly selected student (a) owns a bicycle and a two-wheeler? (b) owns a car, but does not own a bicycle? (c) does not own any of the three? (d) owns a bicycle, but no car or two-wheeler?

Answer 1

a) P(owns a bicycle and two-wheeler) = 0.25 * 0.6 = 0.15

b) P(owns a car and bicycle) = 0.3 * 0.5 = 0.15

P(owns a car but does not own a bicycle) = P(owns a car) - P(owns a car and bicycle)

                                                                  = 0.3 - 0.15 = 0.15

c) P(own a car or bicycle or two wheeler) = 0.3 + 0.6 + 0.3 - 0.15 - 0.15 - 0 + 0

                                                      = 0.9

P(does not own any of the three) = 1 - P(own a car or bicycle or two wheeler)

                                                      = 1 - 0.9 = 0.1

d) P(owns a bicycle but no car or two wheeler) = P(bicycle) - P(bicycle and car) - P(bicycle and two wheeler) = 0.6 - 0.15 - 0.15 = 0.3