Probability Assignment
1. It has been determined that if a person shopping for a new car makes an appointment with salesperson they are more likely to buy a car on the spot. Given the table below and defining thi events as:
A (Sale)
B (Less than two years experience)
|
|
Car Prospect with Appointment
|
|
|
Salesman's Experience
|
Sale
|
No Sale
|
Total
|
|
Less than 2 Years
|
.20
|
.25
|
.45
|
|
2 Years or more
|
.15
|
.40
|
.55
|
|
TOTALS
|
.35
|
.65
|
1.00
|
FIND:
a. P(A ∩ B)
b. P(A I B)
c. P(A U B)
d. P(B I A) {Not necessarily the same as b above}
State which values were found in the above table and which were computed. Include formulas and show work for computed values.
2. In determining what size inventories of two products to have on hand before promoting the sales of one product, it is important to know if sales of the two products are independent. Given that the probability that a customer will buy product A is .6, and the probability that a customer will buy product B is .4, and the probability that a customer will buy either product A or B or both is .7; determine if the sales of the two products are dependent or independent.
3. A security system has two subsystems either of which can dial the police department in the event of a break in. Subsystem A uses ultrasonic waves to detect the presence of a foreign body. Subsystem B employs switches at all windows and doors. If an intrusion occurs, the probability that it will be detected by A is .95 and by B is .90 and by both systems is .89. If there is an intrusion:
a. What is the probability that it will be detected by devices A or B or both?
b. What is the probability that the system won't detect the intrusion?