Question

1. A company is looking into subsidizing its employee’s commute costs and conducts a survey. It finds that 55% of employees use a car. Of those who use a car, 40% have a commute that takes 30 minutes or more. Of those who do not use a car, 10% have a commute that takes 30 minutes or more.
   1. What is the probability that an employee uses a car given that their commute takes 30 minutes or more?
   2. What is the probability that an employee does not use a car and their commute takes less than 30 minutes?
   3. What is the probability that an employee uses a car given that their commute takes less than 30 minutes?

Answer 1

a)

P(takes 30 minute or more)=P(use car and takes 30 minute or more)+P(not use car and takes 30 minute or more)

=0.55*0.4+0.45*0.10=0.2650

hence probability that an employee uses a car given that their commute takes 30 minutes or more

=P(use car and takes 30 minute or more)/P(takes 30 minute or more)=0.55*0.4/0.2650=0.8301890

b)

probability that an employee does not use a car and their commute takes less than 30 minute

=P(not use car and takes 30 minute or less)/P(takes less than 30 minute )

=0.45*(1-0.1)/(1-0.2650)=0.551020

c)

probability that an employee uses a car given that their commute takes less than 30 minutes

=P(use car and takes 30 minute or less)/P(takes less than 30 minute )

=0.55*(1-0.4)/(1-0.2650)=0.448980