View the employee database as the sample space of a random experiment in which an employee is selected at random. That is, each employee represents one outcome, and all possible outcomes are equally likely.

.a) Find the probability of selecting a woman. 28/71

.b) Find the probability that the salary is over $35,000. 58/71

.c) Find the probability that the employee is at training level B. 24/71

.d) Find the probability that the salary is over $35,000 and the employee is at training level B. 22/71

.e) Find the probability that the salary is over $35,000 given that the employee is at training level B. 22/24

.f) Is the event "salary over $35,000" independent of being at training level B? How do you know? Yes; there are salaries under $35,000 with training level B

.g) Find the probability that the salary is over $35,000 given that the employee is at training level C. 9/9

.h) Find the conditional probability of six years or more of experience given female. 4/28

.i) Are the two events "female" and "six years of experience or more" independent? How do you know? Are these two events mutually exclusive? How do you know? Yes; Gender and experience have no relation to each other. No; They can be both at the same time.

.j) Are the two events "training level A" and "training level B" independent?Yes How do you know? One is greater than the other.Are these two events mutually exclusive? YesHow do you know? A cannot be B, which cannot be C

[15]4. You have a position open and are trying to hire a new person. Assume that the mean and standard deviation of the new person's experience will follow a normal distribution with the mean and standard deviation of your 71 current employees (use raw data).

a) Find the probability that the new person will have more than 6 years of experience..4688

b) Find the probability that the new person will have less than 3 years of experience..1984

c) Find the probability that the new person will have between 4 and 7 years of experience..3555

The following questions do not refer to the database anymore.

[19]5. Your firm is considering the introduction of new toothpaste. At a strategy session, it is agreed that a marketing study will be successful with probability 0.65. It is also agreed that the probability of a successful product launch is 0.40. However, given that the marketing study is successful, the probability of a successful product launch is 0.55.

.a) Draw the appropriate decision tree for this situation.

Marketing / Yes / No
0.65 / 0.35
If Marketing Yes / 0.55 / 0.45
If Marketing No / 0.1214 / 0.8786

.

.b) Find the probability that the marketing study is successful and the product launch is successful.

..65 * .55 = .3575

.c) Given that the product launch succeeds, find the conditional probability that the marketing study was favorable. .65

.d) Find the conditional probability that the product launch is successful, given that the marketing study was not successful. .1214

.e) Are the two events "marketing study successful" and "product launch successful" independent? How do you know? No; probability is sensitive to whether or not marketing study is successful.

[16]6. A plane has 23 passenger seats. Based on experience, the operator knows that, on average, 10% of the passengers who book a seat on a given flight do not show up for the flight. As a consequence, the operator usually accepts more bookings that there are seats available.

.a) Given that the operator has accepted 25 reservations for a given flight, find the probability that each passenger that will show up for that flight can be seated. .2659

.b) If this company operates three flights a day and has accepted 25 reservations for each of these flights, find the probability that each passenger that will show up for each of these three flights can be seated. .0188

.c) The company offers$100 compensation to each passenger with a confirmed reservation who cannot find a seat on his or her flight. What is the expected value of the compensation paid for a single flight for which 25 reservations had been taken? $34.30