Probability Questions

TRUE/FALSE

1. Probabilistic techniques include uncertainty and assume that there can be more than one model solution.
2. Objective probabilities that can be stated prior to the occurrence of an event are classical or a priori.
3. The probabilities of mutually exclusive events sum to zero.
4. A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.
5. A continuous random variable may assume only integer values within a given interval.
6. A payoff table is a means of organizing a decision situation, including the payoffs from different decisions given the various states of nature.

FILL IN THE BLANKS

7. Objective probabilities that are stated after the outcomes of an event have been observed are
____________.
8. According to the fundamentals of probability, P(event) must be between ____ and _____, and the probabilities of all events in an experiment must sum to ____.
9. A ________________________ is an organization of numerical data about the events of an experiment.
10. One of the properties of ____________distribution is that the probability of success remains constant over time.
11. The _____________________ of ________________ is the maximum amount a decision maker would be willing to pay for additional information.

PROBLEM SOLVING

12. Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Jim will be accepted by at least one of the two universities?

13. A fair die is rolled 8 times. What is the probability that an even number (2,4, 6) will occur between 2 and 4 times?

14. If X has the following probability distribution:

X 1 2 3 4
P(X) .1 .5 .2 .2

Compute the standard deviation of X.

15. Two Psychology majors, in 2 different sections of Clinical Psychology, were comparing test scores. The following gives the students' scores, class mean, and standard deviation for each section:
Section 1 Section 2
Score 84 75
Mean 75 60
Standard deviation 7 8

What is the z-score of the student from section 1 and what is the probability that a student in section 1 will score higher than 84?

20. A manufacturer must decide whether to build a small or a large plant at a new location. Demand at the location can be either small or large, with probabilities estimated to be 0.4 and 0.6 respectively. If a small plant is built, and demand is large, the production manager may choose to maintain the current size or to expand. The net present value of profits is $223,000 if the firm chooses not to expand. However, if the firm chooses to expand, there is a 50% chance that the net present value of the returns will be 330,000 and 50% chance the estimated net present value of profits will be $210,000. If a small facility is built and demand is small, there is no reason to expand and the net present value of the profits is $200,000. However, if a large facility is built and the demand and the demand turns out to be small, the choice is to do nothing with a net present value of $40,000 or to stimulate demand through local advertising. The response to advertising can be either modest with a probability of .3 or favorable with a probability of .7. If the response to advertising is modest the net present value of the profits is $20,000. However, if the response to advertising is favorable, then the net present value of the profits is $220,000. Finally, the when large plant is built and the demand happens to be high, the net present value of the profits $800,000.

Draw a decision tree.