How is data presented, compared and used to predict future outcomes?
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1 How is data presented, compared and used to predict future outcomes?
2 The standards for this domain MM1D1 Students will determine the number of outcomes related to a given event. MM1D2 Students will use the basic laws of probability. MM1D3 Students will relate samples to a population. MM2D1 Using sample data, students will make informal inferences about population means and standard deviations. MM2D2 Students will determine an algebraic model to quantify the association between two quantitative variables.
3
4 COUNTING PRINCIPLES MM1D1 Addition principle Multiplication principle Permutations & Combinations
5 Addition Principle Torre is choosing an elective for his 6 th period class. He can choose from 2 different band classes, 3 different computer classes and 4 different art classes. How many different possible choices could Torre make for his 6 th period class?
6 Addition Principle Answer Since he can only have one 6 th period class the events are disjoint which means they have no outcomes in common. Applying the addition principle of counting, there are = 9 choices.
7 Multiplication Principle An ice cream shop has 24 flavors of ice cream, 8 different toppings, and 3 different types of ice cream cones. How many different types of ice cream cones can be ordered if each order has to have a topping, ice cream, and a cone?
8 Multiplication Principle Answer Each order has to have a cone, a flavor of ice cream and a topping so the total number of choices are = 576
9 TWO MORE TO TRY Casey is going to buy a car from Budget Motors, Corner Motors, or Viking Motors. Budget Motors sells 10 different models, Corner Motors sells 8 different models, and Viking Motors sells 5 different models of cars. From how many different models of cars can Casey choose? Pete's Pizza offers two types of crusts: thin crust or thick crust, and 4 toppings: beef, chicken, pepperoni, and sausage. How many different ways could you order a pizza with one type of crust and one topping? 23 8
10 Permutations & Combinations A permutation is an arrangement in which the order matters! A combination is an arrangement in which order is NOT important! Factorial n!
11 Permutations order matters If you have 12 pictures and you want to put 4 of them on a photo page, how many different ways can you choose the pictures for the photo page? So you have 12 pictures choosing 4 at a time.
12 Permutations order matters answer It is formally written 12 P 4 Calculated: 12*11*10*9 = 11,880 ways
13 Combinations order does NOT matter If you have 5 letters and want to know how many 2 letter combinations exist.
14 Combinations order does NOT matter answer It is formally written 5 C 2 Calculated: 5 * 4 = 10 2
15 TWO MORE TO TRY There are 8 books on a shelf. If 3 books are chosen at random, how many different groups of 3 books could be chosen? There are 6 students qualified to be chosen as president and vice president for the Recycle-It Club. How many different ways could they be selected as president and vice president for the club? 56 30
16 Ask yourself Does order matter?"
17 QUICK CHECK A swim team has 12 swimmers who can swim in a freestyle event. The swim coach will choose 4 of these swimmers for the freestyle relay race. How can the coach find the number of possible four-person teams from the eligible swimmers? Combination order does NOT matter.
18 QUICK CHECK A swim team has 12 swimmers who can swim in a freestyle event. The swim coach will choose 4 of these swimmers for the freestyle relay race. How can the coach determine the number of different swimmer orders that are possible for the race? Permutation order matters.
19 QUICK CHECK A committee must award 3 students with scholarships. Fifteen students are candidates for the scholarship including you and your two best friends. If the awardees are selected randomly, what is the probability that you and your two best friends win the scholarships? Combination order does NOT matter.
20 QUICK CHECK From a group of 5 doctors and 7 nurses, Ellen must select a committee consisting of 2 doctors and 3 nurses. In how many ways can she do this? Combination order does NOT matter.
21 QUICK CHECK How many different ways can Yvonne stack 6 comic books? Permutation order matters.
22 QUICK CHECK A bag contains 5 cards number 1-5. You draw one card at a time until you draw all 5 cards. What is the probability of drawing a card numbered 1 first and the card numbered 2 second? Permutation order matters.
23 QUICK CHECK Keisha gets to choose 2 prizes from the grab bag containing 10 prizes at the Dentist office. How many ways are 2 prizes possible? Combination order does NOT matter.
24 QUICK CHECK At a busy restaurant, five tables open up at the same time. How many different ways can the hostess seat the next five families waiting to be seated? Permutation order matters.
25 QUICK CHECK Debra can choose from 31 flavors of ice cream. She wants to get a bowl with four different flavors of ice cream. How many different bowls of four scoops are possible? Permutation order matters.
26 More Practice Handout
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