## Math 113: Study Guide - Chapters 3-4

1. Circle all values that can / can not be probabilities.
2. Know the probability of an event certain to happen and the probability of an event that can't happen.
3. Find the probability of an event when one outcome is more likely than the rest. Similar to the dice problem from the side board where the three was two times as likely as every other number.
4. For a described experiment, list all possible outcomes. Then find the probabilities of specific events.
5. Given a probability distribution, find the mean, variance, and standard deviation (use the pdist program on the calculator). Also know which two requirements must be satisfied for the distribution to be a probability distribution. Look at problems 4.2.5-8.
6. Read a news article. Decide if events are mutually exclusive. Decide if events are independent. Decide if the event meets the requirements of a binomial experiment.
7. Work a binomial problem involving passing a test by getting so many questions right. Use the binomial program on the calculator to find the answer.
8. Find the mean and standard deviation of a binomial distribution (look at pg 214).
9. Read a news article. Work with sampling error. Decide if the event meets the requirements of a binomial experiment.
10. Given a joint frequency distribution (see table 3-1), find two joint probabilities, two marginal probabilities, and two conditional probabilities.
11. Given the number and type of candies in a bag, find the probability of selecting a specific color on the first try; on the second try with replacement; on the second try without replacement.
12. Identify whether each experiment is binomial or not. If not, explain why.
13. Simulate an experiment using the calculator or Statdisk. Very similar to the simulation we performed in class where we found the mean number of children that must be born to guarantee at least one of each gender. Make sure you know how to generate random numbers.
14. Identify each pair of events as independent or dependent. Three parts. Look at problems 3.4.1-2
15. Write a concise sentence describing a binomial experiment.
16. Find the expected value of a game. Look at problems 4.2.13-16
17. Find the probability of "at least one" of something given the probability of "none". Read pages 147-148.
18. List all the permutations of a word. Read page 163.
19. Use the fundamental counting principle to find the number of ways a compound experiment can occur.
20. Convert an odds into a probability.

### Notes:

• Where references to the text are given, the problems are similar to, but not identical to problems from the text.
• You may use your calculator, Statdisk, or both on the exam.
 # 1 2 3 4 5 6 7 8 9 10 Pts 3 2 2 6 8 8 3 4 8 12 # 11 12 13 14 15 16 17 18 19 20 Total Pts 9 5 10 6 3 2 2 3 2 2 100