Math 160: Study Guide - Chapters 6-8

1. You are given a Venn diagram and asked to identify the number in an event.
2. Normal probability. Look at problems 8.5.53, 55, 59, 63
3. You are given portions of a joint probability distribution and enough information to complete the table.
4. You are given a joint probability distribution. Use it to find eight probabilities. Look at problems 7.2.1-12 and 7.3.1-12 and the chapter 7 review problems 9-17.
5. Decision Analysis problem. A payoff table is given. Compute the opportunistic loss table. Find the payoff or loss under the expected value, maximax, maximin, and minimax criterions.
6. You are given a situation with conditional probabilities and asked to create a tree diagram. Then complete the joint probability distribution from that and find some probabilities.
7. Binomial problem. Use the calculator program to find binomial probabilities. Also find the mean of the binomial distribution.
8. Determine the number of ways certain events can happen using combinations. One is a simple event and the other is a compound event requiring the multiplication principle.
9. A bag contains different types of bills. Find the probability of a randomly selected bill being of a particular kind. Find the probability of the second bill being of a particular kind if you replace the first, don't replace the first but know what it was, and don't replace the first and don't know what it was.
10. Bayesian problem. Create a joint probability distribution from the information given. Then find some probabilities. Some of the probabilities are marginals, some are joint, some are conditional. You need to be able to figure out which is which by reading the problem. Look at problems 7.4.43-52.
11. Find the probability of a certain poker hand occurring. The problem has been modified by removing some of the cards from the deck, so be careful. Look at problems 7.1.23-26, 63-70. Show the setup if you want partial credit. You may use the hypergeometric program to find the probabilities for you. These are simpler probabilities, not things like "full house" or "three of a kind".
12. Finish a series of a game. Create a tree diagram, find the probability that the series goes until a certain number of games, find the probability each team wins. Look at problem 7.3.42.

Notes

• Portions of problems 10 - 12 will be sent home with you prior to the actual exam. There are problems there that will need to be set up and completed before the actual exam. You will use the results of the take home exam to answer more questions on the in-class exam. If you try to wait until the actual exam to complete all of the exam, you will run out of time.
• You are encouraged to work in a group to complete the portion sent home with you to ensure you have the correct answers. You may work in groups of up to three people on the take-home portion.
• In the points per problem below, the notation 6+9 means that 6 points will be from the in-class portion and 9 points will be from the take-home portion.

Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 Total 6 3 4 16 10 10 8 4 4 5+5 10 6+9 100