Math 160: Study Guide - Chapters 7&8

  1. You are given a Venn diagram and asked to interpret it. For each question, rewrite the statement mathematically and then find the answer. For example: Let R represent someone being a Republican and H represent someone who likes the healthcare reform. If the question was "How many people were Republicans but do not like healthcare reform?", then you would write n(R∩H') and then find the number from the Venn diagram. If the question was "Find the probability that someone is not Republican or does not like healthcare reform" then you would write P(R'UH').
  2. Complete the truth table for the given statements.
  3. You are given a joint probability distribution. Use it to find the indicated probabilities. Identify whether certain events are independent or dependent.
  4. 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.
  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. 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.
  7. Determine the number of ways you can form words or numbers that satisify the requirements. Three parts.
  8. 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.
  9. 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.
  10. 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.
  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. Part of this is given as a take home exam to save time on the test.
  12. Find the expected value of a game. How much should the person pay to make it a fair game?


Points per problem

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