# Math 113: Study Guide - Chapters 3-4

1. Circle all values that can / can not be probabilities.
2. Find the probability of an event when one outcome is more likely than another.
3. Find the probability of an event when some of the outcomes are more likely than the rest.
4. For a described experiment, list all possible outcomes. Then find the probabilities of specific events.
5. Given a probability distribution, find the value of one of the probabilities to make it a probability distribution, and the mean, variance, and standard deviation (use the pdist program on the calculator). Look at problems 4.2.3-8.
6. Read the summary of a news release. Decide if the questions satisfy the conditions of a binomial experiment.
7. Write a concise sentence describing a binomial experiment.
8. Find the mean and standard deviation of a binomial distribution. Look at problems 4.4.5-16.
9. 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.
10. Find the probability of "at least one" of something given the probability of "none". Read pages 144-145 on complements.
11. Read a news article. Work with sampling error. Decide if the event meets the requirements of a binomial experiment.
12. 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.
13. Given a joint frequency distribution (see table 3-1 on pg 113 for an example), find the probabilities. The probabilities can be joint, marginal, conditional, or involve compound events. Seven parts. Leave your answer in fractional form.
14. Identify whether each experiment is binomial or not. Six 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. List all the permutations of a word. Read pages 159-160.
17. 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.
18. Use the fundamental counting principle to find the number of ways a compound experiment can occur.
19. Convert an odds into a probability.
20. 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 one of each gender. After generating the data, find the mean and standard deviation.

## 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.
• Problem 20 is a take home problem. It is given to you as a take home just so you have plenty of time in class to answer the other questions. It is due the day of the exam.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total 3 2 3 7 5 4 3 4 4 3 6 3 14 12 6 3 6 3 3 6 100