Five-Minute Check (over Lesson 12–5) Mathematical Practices Then/Now New Vocabulary Example 1: Real-World Example: Identify Mutually Exclusive Events Key Concept: Probability of Mutually Exclusive Events Example 2: Real-World Example: Mutually Exclusive Events Key Concept: Probability of Events That Are Not Mutually Exclusive Example 3: Real-World Example: Events That Are Not Mutually Exclusive Lesson Menu

Determine whether the event is independent or dependent Determine whether the event is independent or dependent. Samson ate a piece of fruit randomly from a basket that contained apples, bananas, and pears. Then Susan ate a second piece from the basket. A. independent B. dependent 5-Minute Check 1

Determine whether the event is independent or dependent Determine whether the event is independent or dependent. Kimra received a passing score on the mathematics portion of her state graduation test. A week later, she received a passing score on the reading portion of the test. A. independent B. dependent 5-Minute Check 2

A spinner with 4 congruent sectors labeled 1–4 is spun A spinner with 4 congruent sectors labeled 1–4 is spun. Then a die is rolled. What is the probability of getting even numbers on both events? A. 1 B. C. D. 5-Minute Check 3

Two representatives will be randomly chosen from a class of 20 students. What is the probability that Janet will be selected first and Erica will be selected second? A. B. C. D. 5-Minute Check 4

A bag contains 21 marbles. Six of these are red A bag contains 21 marbles. Six of these are red. Two students each draw a marble from the bag without looking. What is the probability they will both draw a red marble? A. B. C. D. 5-Minute Check 4

Mathematical Practices 1 Make sense of problems and persevere in solving them. 4 Construct viable arguments and critique the reasoning of others. Content Standards S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. MP

You found probabilities of independent and dependent events. Apply the addition rule to situations involving mutually exclusive events. Apply the addition rule to situations involving events that are not mutually exclusive. Then/Now

mutually exclusive events Vocabulary

Identify Mutually Exclusive Events A. CARDS Han draws one card from a standard deck. Determine whether drawing an ace or a 9 is mutually exclusive or not mutually exclusive. Explain your reasoning. Answer: These events are mutually exclusive. There are no common outcomes. A card cannot be both an ace and a 9. Example 1A

Identify Mutually Exclusive Events B. CARDS Han draws one card from a standard deck. Determine whether drawing a king or a club is mutually exclusive or not mutually exclusive. Explain your reasoning. Answer: These events are not mutually exclusive. A king that is a club is an outcome that both events have in common. Example 1B

A. The events are mutually exclusive. A. For a Halloween grab bag, Mrs. Roth has thrown in 10 caramel candy bars, 15 peanut butter candy bars, and 5 apples to have a healthy option. Determine whether drawing a candy bar or an apple is mutually exclusive or not mutually exclusive. A. The events are mutually exclusive. B. The events are not mutually exclusive. Example 1A

A. The events are mutually exclusive. B. For a Halloween grab bag, Mrs. Roth has thrown in 10 caramel candy bars, 15 peanut butter candy bars, and 5 apples to have a healthy option. Determine whether drawing a candy bar or something with caramel is mutually exclusive or not mutually exclusive. A. The events are mutually exclusive. B. The events are not mutually exclusive. Example 1B

Concept

Let Q represent picking a quarter. Let P represent picking a penny. Mutually Exclusive Events COINS Trevor reaches into a can that contains 30 quarters, 25 dimes, 40 nickels, and 15 pennies. What is the probability that the first coin he picks is a quarter or a penny? These events are mutually exclusive, since the coin picked cannot be both a quarter or a penny. Let Q represent picking a quarter. Let P represent picking a penny. There are a total of 30 + 25 + 40 + 15 or 110 coins. Example 2

P(Q or P) = P(Q) + P(P) Probability of mutually exclusive events Simplify. Answer: or about 41% ___ 9 22 Example 2

MARBLES Hideki collects colored marbles so he can play with his friends. The local marble store has a grab bag that has 15 red marbles, 20 blue marbles, 3 yellow marbles and 5 mixed color marbles. If he reaches into a grab bag and selects a marble, what is the probability that he selects a red or a mixed color marble? A. B. C. D. Example 2

Concept

Events That Are Not Mutually Exclusive ART Use the table below. What is the probability that Namiko selects an acrylic or a still life? Since some of Namiko’s paintings are both acrylics and still life, these events are not mutually exclusive. Use the rule for two events that are not mutually exclusive. The total number of paintings from which to choose is 30. Example 3

Let A represent acrylics and S represent still life. Events That Are Not Mutually Exclusive Let A represent acrylics and S represent still life. P(A or S) = P(A) + P(S) – P(A and S) Substitution Simplify. Answer: The probability that Namiko selects an an acrylic or a still life is or about 40%. Example 3

SPORTS Use the table. What is the probability that if a high school athlete is selected at random that the student will be a sophomore or a basketball player? A. B. C. D. Example 3