## 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 four was four times as likely as every other number.
4. For a described experiment, list all possible outcomes. Then find the probabilities of specific events.
5. Write a concise sentence describing a binomial experiment.
6. 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 4.2.3-8.
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. Read the summary of a news release. Decide if the questions satisfy the conditions of a binomial experiment.
9. Find the mean and standard deviation of a binomial distribution. Look at problems 4.4.5-16.
10. 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. Four parts.
11. Find the probability of "at least one" of something given the probability of "none". Read pages 144-145 on complements.
12. Read a news article. Work with sampling error. Decide if the event meets the requirements of a binomial experiment. List examples of non-sampling error given in the article.
13. Given a joint frequency distribution (see table 3-1 on pg 113 for an example), find two joint probabilities, two marginal probabilities, two conditional probabilities, and one "or" probability.
14. Identify whether each experiment is binomial or not. Five parts. If not, explain why.
15. Identify each pair of events as independent or dependent. Three parts. Look at problems 3.4.1-2
16. Simulate an experiment using the computer. 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 two of each gender. After generating the data, find the mean and standard deviation.
17. List all the permutations of a word. Read pages 159-160.
18. Find the expected value of a game. Look at problems 4.2.13-16. The expected value of a probability distribution is the same thing as its mean, so you could use the pdist program.
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.

Point values for problems
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Tot 3 2 3 6 3 5 3 2 4 8 3 7 14 10 6 9 3 3 3 3 100