Probability, Permutations, & Combinations LESSON 11.1
Objective Define probability Use the counting principle Know the difference between combination and permutation Find probability
Probability PROBABILITY: the measure of the likeliness of an event # of ways to win # of ways to play
Probability 1a. What is the probability of rolling a 4 on a 6-sided die? 1b. What is the probability of rolling an even number on a 6-sided die?
Probability 2. A bag of candy contains 12 red, 11 yellow, 5 green, 6 orange, 5 blue, and 16 brown candies. a.) What is the probability that you will randomly draw a yellow candy from the bag? b.) What is the probability that you will NOT draw an orange candy from the bag?
Sample Space Sample Space is a visual representation of all possible outcomes. 3a. We are going to flip a coin 3 times. Find the sample space.
Sample Space 3b. How many outcomes give us at least 2 heads? 3c. Find the probability of getting at least 2 heads.
Permutation & Combination If a sample set is too large to list, the number of outcomes and successes can be determined using permutations and combinations. Permutations ORDER MATTERS Combinations order DOES NOT matter
Permutation Permutation ORDER MATTERS To calculate the number of permutations, multiply the number of choices possible for each position. This is called the Counting Principle.
Permutation 4a. On a 3-question multiple choice quiz, how many different quizzes could be turned in if there are 4 options (a,b,c,d)? 4b. How many different quizzes could be turned in if no answers were repeated?
Permutation To calculate permutation without repetition: np r = P n, r = n! n r! where n is the number of objects to choose from and r is the number of object being selected.
Permutation Permutations can be calculated with a calculator. a) Type the value of n b) [MATH] PRB npr c) Type the value of r and press enter TRY IT! 5a. P(5,3) b. P(16,5) c. P(25,13)
Combination Combination order DOES NOT matter, *object may be repeated nc r = C n, r = n! n r! r!
Combination Combinations can be calculated with a calculator. a) Type the value of n b) [MATH] PRB ncr c) Type the value of r and press enter TRY IT! 6a. C(5,3) b. C(16,5) c. C(25,13)
Combination 7. Mrs. Mann is picking 4 students to be team leaders. There are 25 students in the class. How many different ways can she pick the 4 students?
Combination 8. Super Generic Ice Cream Shoppe has 9 different flavors to put in your ice cream. You can choose 3 flavors to put in a single dish. How many different flavor combinations can you create?
Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of 10 c. Class presidency 1 st is president, 2 nd is VP, etc. d. Draw a hand of 6 cards from a deck of cards e. Number of ways to make a license plate
Permutation & Combination THINK! Identify if order matters or doesn t matter FIRST Permutations can use the counting principle, combinations don t Generally: Two things at once Combination One after the other - Permutation
Permutation & Combination 10. There are 6 students presenting projects in a history class. The teacher is randomly determining the order in which the students will present. Each student only presents once. Brooke is one of the six students. What is the probability that Brooke will present first?
Compound Probabilities If more then 1 event is happening, it creates a Compound Probability. If independent - P AandB = P A P(B) If dependent - P AandB = P A P(BfollowingA)
Compound Probabilities 11. From a deck of 52 cards, 3 cards are randomly chosen. They are a 10, Jack, and another 10, in that order. a. Find the probability that this event occurs if each card is replaced after drawn. b. Find the probability that this even occurs if each card is NOT replaced each time.
Probability 12. The table bellow lists the items in Jana s closet. She randomly selects 2 items. What is the probability that she will select 2 shirts? Item Number of Each Color Black Blue White Red Purple Shirt 2 3 1 5 5 Shoes 3 0 1 2 2
Probability 13. There are 4 nickels, 3 dimes, and 5 quarters in a purse. Find the probability. a. P(1 dime, then 1 nickel, then another dime) without replacement b. P(drawing 3 coins and getting 1 of each)
Homework Worksheet 11.1