AP Statistics 6.2 Probability Models Examples

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AP Statistics – 6.2 Probability Models – Examples Sample Space, Multiplication Rule of Counting, & Tree Diagrams

1. At a local cafeteria your meat choices are ham (H) or chicken (c) or beef steak (S). And, with each meat choice you may choose potatoes, either baked (B) or mashed (M). a. List the sample space. b. Create a tree diagram to find all the possible choices. c. Determine the number of possible meat and potato dinner combinations (Multiplication Rule and Tree Diagram).

2. From a bowl that contains ten slips of paper numbered 0,1,2,3,4,5,6,7,8, and 9, you select two slips at random, one at a time, with replacement. How many ordered samples are possible?

3. Assume that you roll a 4-sided die three times. How many ordered outcomes are possible?

4. A bowl contains three slips of paper numbered 1, 2, 3. a. Find the number of possible ordered samples of size 3, sampling without replacement. b. Create a tree diagram to find all the possible choices. c. List the sample space.

5. A bowl contains 4 slips of paper numbered 1, 2, 3, 4. a. Create a tree diagram to list all the possible choices of size two without replacement. b. Find the number of ordered samples of size 2 that can be selected without replacement from this bowl. c. List all the possible outcomes. Name: Date: Block:

AP Statistics – 6.2 Probability Models – Examples

General Probability 1. A typical roulette wheel used in a casino has 38 slots numbered 1, 2, 3, …, 36, 0, 00. The 0 and 00 slots are colored green. Half of the remaining slots are red and the other half are black. Also, half of the integers between 1 and 36 are odd and half are even, with 0 and 00 defined as neither even nor odd. A ball is rolled around the wheel and ends up in one of the slots. Let A  {red}, B  {0,00} , C  {14,15,16,17,18}. a. Assuming you are only interested in color of the outcomes, what is the sample space? b. Assuming you are playing one time. Find the following probabilities. i. P( A) = ii. P(B) = iii. P(C) = c. Assuming you are playing two times. Find the following probabilities. i. P(B  C)  ii. P(B  C)  iii. P(C  C)  iv. P(B  B) 

2. Suppose that 40% of cars in your area are manufactured in the United States, 30% in Japan, 10% in Germany, and 20% in other countries. If cars are selected at random, find the probability that: a. A car is not U.S.-made. b. It is made in Japan or Germany c. You see two in a row from Japan d. None of three cars came from Germany. e. At least one of three cars is U.S.-made. f. The first Japanese car is the fourth one you chose.

3. Five multiple choice questions, each with four possible answers, appear on your history exam. a. Define the sample space. b. What is the probability that if you guess, you i. Get none of the questions correct? ii. Get all of the questions correct? iii. Get at least one of the question wrong? iv. Get your first incorrect answer on the fourth question?