1. Transparency 9 Click the mouse button or press the Space Bar to display the answers.

2. Transparency 9a

3. 9-4 Compound Events

4. Video Tutor Help Probability of Independent Events Probability of Dependent Events Probability of Dependent Events Khan Academy Brain Pop Probability Probability of compound events

5. Video Tutor Help Finding the probability of the complement of an even

6. Worksheets Daily Notetaking Guide Worksheets Version A Practice, Guided Problem Solving Lesson 9-4 Practice 9-4 Guided Problem Solving 9-4

7. Vocabulary Practice Vocabulary 9A: Graphic Organizer Vocabulary 9B: Reading Comprehension Vocabulary 9C: Reading/Writing Math Symbols Vocabulary 9D: Visual Vocabulary Practice Vocabulary 9E: Vocabulary C Vocabulary 9F: Vocabulary Review Puzzle Vocabulary (Electronic) Flash Cards Patterns and Rules

8. Additional Lesson Examples Step-by-Step Examples Lesson 9-4

9. Lesson Readiness Lesson Quiz Problem of the Day Lesson 9-4

13. Compound Events The combined action of rolling a number cube and spinning a spinner is a compound event. In general, a compound event consists of two or more simple events.

14. Independent events The outcome of the spinner does not depend on the outcome of the number cube. These events are independent. For independent events the outcome of one event does not affect the other event.

15. Probability of Independent Events Words: The probability of two independent events can be found by multiplying the probability of the first event by the probability of the second event. Symbols: P(A and B) = P(A) * P(B)

16. Dependent Events If the outcome of one event affects the outcome of another event, the compound events are called dependent events.

17. Probability of Dependent Events Words: If two events, A and B, are dependent, then the probability of both events occurring is the product of the probability of A and the probability of B after A occurs. Symbols:P(A and B) = P(A) * P(B following A)

18. Mutually Exclusive Events Two events that cannot happen at the same time are mutually exclusive. For example, when you roll two number cubes, you cannot roll a sum that is both 5 and even. So, P(A or B) = 4 36 18 36 + 18 11 =

20. A box contains the same number of green marbles, orange marbles, and blue marbles. You draw one marble, replace it, and draw a second marble. What is the probability that both marbles you draw are blue? LESSON 9-4 Since of the marbles are blue, the probability of drawing a blue marble is. 1313 1313 P(blue, then blue)= P(blue)  P(blue) Selecting blue is the first and second event. Substitute. =  1313 1313 Multiply. = 1919 The probability that both marbles will be blue is. 1919 Compound Events Additional Examples

21. Example 9-1a Games In a popular dice game, the highest possible score in a single turn is a roll of five of a kind. After rolling one five of a kind, every other five of a kind you roll earns 100 points. What is the probability of rolling two five of a kinds in a row? The events are independent since each roll of the dice does not affect the outcome of the next roll. There are six ways to roll five of a kind, (1, 1, 1, 1, 1), ( 2, 2, 2, 2, 2 ), and so on, and there are 6 5 or 7776 ways to roll five dice. So, the probability of rolling five of a kind on a toss of the dice isor. Probability of Independent Events

22. Example 9-1b P( two five of a kind ) = P( five of a kind on first roll ) P( five of a kind on second roll ) Answer: The probability of rolling two five of a kind in a row is

26. Example 9-2a Shirts Charlie’s clothes closet contains 3 blue shirts, 10 white shirts, and 7 striped shirts. What is the probability that Charlie will reach in and randomly select a white shirt followed by a striped shirt? Answer:The probability Charlie will select a white shirt followed by a striped shirt is 10 of 20 shirts are white. 7 of 19 remaining shirts are striped. Probability of Dependent Events

27. You select a card at random from those having A, E, I, O, U, P, C. The card has the letter E. Without replacing the E card, you select a second card. Find the probability of selecting a card that does not have a vowel. LESSON 9-4 There are 6 cards remaining after selecting an E card. P(not vowel) = 2626 number of cards not a vowel number of cards remaining Simplify. 1313 P(not vowel) = The probability of selecting a non-vowel for the second card is. 1313 Compound Events Additional Examples

29. A bag contains 3 red marbles, 4 white marbles, and 1 blue marble. You draw one marble. Without replacing it, you draw a second marble. What is the probability that the two marbles you draw are red and white? LESSON 9-4 The two events are dependent. After the first selection, there are 7 marbles to choose from. P(red, then white)= P(red)  P(white after red) Use the formula for dependent events. Substitute. =  3838 4747 Compound Events Additional Examples

30. (continued) LESSON 9-4 Simplify. = 3 14 The probability that the two marbles are red and white is. 3 14 Multiply.= 12 56 Compound Events Additional Examples

31. Example 5-3a There are 4 red, 8 yellow, and 6 blue socks in a drawer. Once a sock is selected, it is not replaced. Find the probability that two blue socks are chosen. total number of socks after one blue sock is removed number of blue socks after one blue sock is removed Since the first sock is not replaced, the first event affects the second event. These are dependent events. number of blue socks total number of socks Assume first sock picked is blue Probability of Dependent Events

32. Example 5-3a Answer: 1 3