# Math 160: Study Guide - Chapters 7&8

1. You are given a Venn diagram and asked to interpret it.
2. Complete the truth table for the given statements.
3. You are given English statements and then asked to interpret some logical statement involving them. For example pqq
4. You are given a joint probability distribution. Use it to find the indicated probabilities. Identify whether certain events are independent or dependent.
5. 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. Find the probability of a second bill being a certain type without knowing what the first type was. Find the probability of the first bill being a particular kind if you know what the second bill was.
6. 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.
7. A scenario and counting formula (with numbers supplied) are given.Evaluate the expression and interpret the result within the context of the scenario.
8. Determine the number of ways certain events can happen using combinations. Similar to the problem where there were 6 women and 5 men vying for 5 positions. Three parts.
9. Determine the number of ways you can form words or numbers that satisify the requirements. Three parts.
10. You are given the probabilities of some events. Use the multiplication rule to find the probabilities of compound events. For example, you may be given the probabilities of events A, B, and C and asked to find the probability that all three occur or that A and B but not C occur, etc.
11. 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. Part of this is given as a take home exam to save time on the test.
12. Find the number of ways a certain poker hand can occur. The problem has been modified by removing some of the cards from the deck, so be careful. Show the setup if you want partial credit. You may use the hypergeometric program to find the values, but you only want the numerator. These are simpler probabilities, not things like "full house" or "three of a kind". Part of this is given as a take home exam to save time on the test.
13. 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. Part of this is given as a take home exam to save time on the test.
14. Find the expected value of a game. How much should the person pay to make it a fair game?

## Notes

• Portions of problems 11-13 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 7+6 means that 7 points will be from the in-class portion and 6 points will be from the take-home portion.
• A tree diagram was given to you, but if you mess it up, you may want to start over with a new one rather than trying to erase and fix it. Here is a blank tree diagram for the Cubs vs White Sox question.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total 14 8 2 14 10 10 2 6 6 8 12+3 14+3 6+3 4 125