## Math 160: Chapter 6/7 Study Guide

1. You are given a Venn diagram and asked to identify the number in an event.
2. Define the terms given. Know the definitions of Mutually exclusive events, independent events, equally likely events, all inclusive events, and fair game.
3. Normal probability. Look at problems 7.6.53, 55, 59, 63
4. You are given portions of a joint probability distribution and enough information to complete the table. Complete the table, and then find six probabilities. Be able to tell if two events are independent. Look at 6.5.1 - 6.5.16.
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. Statistics problem. Given a set of data, find the mean, median, range, and sample standard deviation.
7. Binomial problem. Use the calculator program to find binomial probabilities. Also find the mean of the binomial distribution.
8. Find the probability of poker hands. The problem has been modified by removing some of the cards from the deck, so be careful. Look at problems 6.3.63 - 6.3.70. Show the setup and find the answer. You may use the hypergeometric program to find the probabilities for you.
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 6.6.43 - 6.6.51.
11. 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 6.5.42.

### Notes:

• Problems 1 - 7 must be worked individually.
• Problems 8 - 11 may be worked in groups of up to three people.
• You must turn in the first portion of the exam before getting into groups.
• You will want to work through the first part of the test as quickly as possible, the group portion will be long.
 # 1 2 3 4 5 6 7 8 9 10 11 Total Pts 6 6 6 12 10 8 12 10 10 10 10 100