2. In a student community, 30% of the students own a car and 50% of the students who own a
the car also owns a bicycle. Also, 60% of the student community on 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.
(a) What is the probability that a randomly selected student owns a car and a bicycle?
(b) What is the probability that a randomly selected student owns a bicycle, but does not
own a car?
(c) What is the probability that a randomly selected student does not own any of the three?
(d) What is the probability that a randomly selected student owns a bicycle, but no car or
two-wheeler
Answers
Given : 30% of the students own a car and 50% of the students who own a the car also owns a bicycle.
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.
To Find : a) What is the probability that a randomly selected student owns a car and a bicycle?
(b) What is the probability that a randomly selected student owns a bicycle, but does not own a car?
(c) What is the probability that a randomly selected student does not own any of the three?
(d) What is the probability that a randomly selected student owns a bicycle, but no car or two-wheeler
Solution:
Let say Total Students = 100S
30% of the students own a car
=> Students owing car = 30S
50% of the students who own a the car also owns a bicycle
=> 15S students own car and bicycle
Car owners do not own two-wheelers.
0 = Car and two-wheelers.
60% of the student community on a bicycle
= Bicycle = 60S
25% of students who own a bicycle, also own a two-wheeler.
=> 15S Bicycle and Two wheelers
30% of the students own a two-wheeler.
30S own two wheeler
probability that a randomly selected student owns a car and a bicycle
= 15S/100S
= 3/20
probability that a randomly selected student owns a bicycle, but does not
own a car = (60S - 15S)/100S = 45S/100S
= 9/20
100S = 30S + 60S + 30S - 15S - 15S - 0 + 0 + None
=> None = 10S
probability that a randomly selected student does not own any of the three = 10S/100S
= 1/10
probability that a randomly selected student owns a bicycle, but no car or
two-wheeler = 30S/100S = 3/10
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