Probability Homework 1

1.A large firm has 85% of its service calls made by a contractor, and 10 of these calls result in customer complaints. The other 15% of the service calls are made by their own employees, and these calls have a 5% complaint rate. Find the:

a) Probabiltiy of receiving a complaint

b) Probability that the complaint was from a customer serviced by the contractor

2.  A car rental agency has 19 compact cars and 12 intermediate-size cars. If four of the cars are randomly selected for a safety check, what is the probability of getting two of each kind? 

3.   The probabilities that a satellite launching rocket will explode during lift-off or have its guidance system fail in the flight are 0.0002 and 0.0005, respectively. Assuming independence find the probabilities that such a rocket will

a) not explode during lift-off;

b) explode during lift-off or have its guidance system fail in flight;

c) neither explode during lift-off nor have its guidance system fail in flight.

4. Suppose that the probability that Ahmad and Mohammad will succeed in assembling the computer are 56% and 71% respectively and that the probability that both will succeed is 39%. Then compute the probability that Mohammad will not succeed in assembling the computer given that Ahmad has not succeeded in assembling the compute