1. Lesson 8-2 Counting Outcomes

2. Definitions Tree Diagram-An organized list to help you determine the number of possible combinations or outcomes.

3. Draw a tree diagram to determine the number of different bicycles from the example. 12 outcomes Mt. Bike 10- Spd Red Black Green 26 in. 28 in. 26 in. 28 in. 26 in. 28 in. Red Black Green 26 in. 28 in. 26 in. 28 in. 26 in. 28 in. Mt., Red 26 in Mt., Red 28 in Mt., Black 26 in Mt., Black 28 in Mt., Green 26 in Mt., Green 28 in 10-Spd., Red 26 in 10-Spd., Red 28 in 10-Spd., Black 26 in 10-Spd., Black 28 in 10-Spd., Green 26 in 10-Spd., Green 28 in Dynamo Bicycles are the Best! Choose your Dynamo Today! Styles: Mountain or 10-Speed Colors: Red, Black or Green Sizes: 26-inch or 28-inch

4. A flea market vendor sells new and used books for adults and teens. Today she has fantasy novels and poetry collections to choose from. Draw a tree diagram to determine the number of categories of books. N U A T A T F P A T A T F P N,F,A N,F,T N,P,A N,P,T U,F,A U,F,T U,P,A U,P,T 8 outcomes

5. Definitions Fundamental Counting Principle- If event M can occur in m ways and is followed by event N that can occur in n ways, then event M followed by event N can occur in m  n ways.

6. In the United States, radio and television stations use call letters that start with K or W. How many different call letters with 4 letters are possible? Number of possible letters for the first letter. 2 Number of possible letters for the second letter. X 26 Number of possible letters for the third letter. X 26 Number of possible letters for the fourth letter. X 26 Total number of possible call letters = 35,152

7. A manager assigns different codes to all the tables in a restaurant to make it easier for the wait staff to identify them. Each code consists of the vowel A, E, I, O or U, followed by two digits from 0 to 9. How many codes could the manager assign using this method? Number of possible vowels for the table code 5 Number of possible digits for the first number of table code X 10 Number of possible digits for the second number of table code X 10 Total number of possible table codes = 500

8. What is the probability of winning a lottery game where the winning number is made up of three digits from 0 to 9 chosen at random? Choices for the first digit. 10 Choices for the second digit. X 10 Choices for the third digit. X 10 Total number of outcomes = 1000 First, find the number of possible outcomes using the Fundamental Counting Principle. There are 1000 possible outcomes. There is 1 winning number. So, the probability of winning with one ticket is 1/1000. This can also be written at a decimal, 0.001 or a percent, 0.1%.

9. What is the probability that Carlyn will guess her friend’s computer password on the first try if all she knows is that it consists of three letters? Choices for the first letter. 26 Choices for the second Letter. X 26 Choices for the third letter. X 26 Total number of outcomes = 17,576 First, find the number of possible outcomes using the Fundamental Counting Principle. There are 17,576 possible outcomes. You get one try to guess it. So, the probability of guessing in one try is 1/17,576.