4. If you were to flip a coin 2 times, list all possible outcomes (order of outcomes does not matter):

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1 Probability: Sample Space: Permutations: Combinations: 1. The probability of rolling a 4 on a six-sided die: 2. The probability of rolling an even number on a die: 3. If you were to flip a coin 1 time, list all possible outcomes: a. What is the probability of getting 1 head/0 tail? b. What is the probability of getting 0 head/1 tail? 4. If you were to flip a coin 2 times, list all possible outcomes (order of outcomes does not matter): a. What is the probability of getting 2 head/0 tail? b. What is the probability of getting 1 head/1 tail? c. What is the probability of getting 0 head/2 tail?

2 5. If you were to flip a coin 3 times, list all possible outcomes (order of outcomes does not matter): a. What is the probability of getting 3 head/0 tail? b. What is the probability of getting 2 head/1 tail? c. What is the probability of getting 1 head/2 tail? d. What is the probability of getting 0 head/3 tail? 6. If you were to flip a coin 4 times, list all possible outcomes (order of outcomes does not matter): a. What is the probability of getting 4 head/0 tail? b. What is the probability of getting 3 head/1 tail? c. What is the probability of getting 2 head/2 tail? d. What is the probability of getting 1 head/3 tail? e. What is the probability of getting 0 head/4 tail?

3 Questions: 1. What happened to the size of the sample space for each additional flip of the coin? 2. What is the difference between a permutation and combination? 3. Why are these outcomes considered combinations? 4. What is the sample space for flipping a coin 3 times where order of the flips does matter? a. What is the probability of flipping at least 2 heads? b. What is the probability of flipping at most 2 tails? c. What is the probability of heads being your first flip?

4 Sample Space Practice: 1. What is the sample space for combinations of rolling two equal dice? 2. What is the probability of rolling a multiple of 4? 3. What is the probability of rolling a sum of 6? 4. Which roll has the highest probability of occurring? 5. What is the sample space for permutations of rolling two equal dice? 6. What is the probability of rolling a 4 on one die and a 6 on the other? 7. What is the probability of rolling an even number on one die and a 3 on the other?

5 Now, what if you needed to determine very large sample spaces? Example 1. In how many different ways can ten dogs line up to be groomed? a. One of the ten dogs is an English Bulldog (love!). What is the probability that the bulldog will be first in line? 2. In how many ways can you arrange six trophies on a shelf? 3. There are 10 basketball teams in the league. There are 3 prizes (1 st place, 2 nd place, and 3 rd place) for the top 3 teams. How many ways can these teams finish? 4. There are 15 members of student council. How many ways can a president, vice-president, and treasurer be elected if each person gets one vote? a. Kyle is running for president. If Kyle wins the presidency, how many ways can the other offices be elected?

6 Permutation Formula: 5. Seven boats enter a race. First, second, and third places will be given to the three fastest boats. How many ways can they finish? a. The Alge-boat has entered the race. What is the probability that Alge-boat will finish in second place? 6. Find the number of ways that the letters in the word HUBBUB can be arranged. 7. Find the number of ways that the letters in the word PRINCIPLE can be arranged. 8. Fifteen students ask to visit the admissions representative from State University. Each visit includes one student. In how many ways can ten time slots be assigned? a. If Sarah Maria is one of the students, what is the probability she will get the second time slot?

7 Review of Probability so far 1. How do you calculate the probability of a simple event (such as rolling a 2 on a die)? 2. What is sample space? 3. What is the Counting Principle? a. You are taking a test that has 5 True/False questions. If you answer each question with True or False and leave none of them blank, how many different ways can you answer the whole test? b. When packing for a business trip, Mr. Simmons selects 3 suits, 4 shirts, and 5 ties. How many different outfits (consisting of 1 suit, 1 shirt, and 1 tie) can he put together? c. The science class decided to present a pet display for the kindergarteners. 2 students volunteered to bring fish; 3 could bring cats; 3 wanted to bring dogs, and 2 said that they could bring rabbits. If the display included one pet from each category, how many displays were possible? d. A popular car model comes in 5 different colors, with a standard or automatic transmission, and with or without a sports package. How many different types of cars are available in this model? 4. How do you calculate the probabilities of consecutive events? a. What is the probability of rolling a 4 on one die and an even number on another? b. What is the probability of flipping heads on one coin and tails on another? c. What is the probability of rolling a 5 on one die and a 6 on another?

8 Combination Formula: 1. A reading list for a course in world literature has 20 books on it. How many ways can you choose 4 books to read? 2. Ten candidates are running for three representative seats. You may vote for up to three candidates. In how many ways can you vote for three or fewer candidates? 3. For a band camp, you can choose two or three roommates from a group of twenty five friends. In how many ways can you choose? 4. A salad bar offers eight choices of toppings for lettuce. In how many ways can you choose four or five toppings? 5. Evaluate the following: a. 6 C 2 b. 8 C 5 c. 4 C 3