1. 1. You choose an O. 2. You choose an M. You choose a card at random from a bag which contains cards with the letters in the word MONOPOLY. Find the probability. Lesson 12.8 , For use with pages 694-700 ANSWER 3 8 ANSWER 1 8

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4. Dependent & Independent Events Section 12. 8

9. GUIDED PRACTICE for Examples 1and 2 In Exercises 1 and 2 , tell whether the events are independent or dependent. Explain your reasoning. 1. You toss a coin. Then you roll a number cube. You randomly choose 1 of 10 marbles. Then you randomly choose one of the remaining 9 marbles. 2. The coins toss does not affect the roll of a dice, so the events are independent. ANSWER There is one fewer number in the bag for the second draw, so the events are dependent. ANSWER

11. EXAMPLE 2 Standardized Test Practice The tosses are independent events, because the outcome of a toss does not affect the probability of the next toss resulting in a win. So the probability of each event is . 1 25 ANSWER The probability of two winning tosses in a row is . 625 1 The correct answer is A . P ( win and win ) = P ( win ) P ( win ) 25 1 1 25 =

12. GUIDED PRACTICE for Examples 1and 2 3. You toss a coin twice. Find the probability of getting two heads. P ( head and head ) = P ( head ) P ( head ) = 1 4 or 25% 1 2 1 2 = The tosses are independent events, because the outcome of a toss does not affect the probability of the next toss ANSWER

13. Daily Homework Quiz For use after Lesson 12. 8 5/10 x 4/9 2. A bag contains ten cards numbered 1 through 10 . You pick one card and then another without replacement. What is the probability that both cards display a value of 6 or higher? ANSWER 2 9 – , 0.2

14. Daily Homework Quiz For use after Lesson 12. 8 1. Events A and B are independent. P(A & B) = P(A) x P(B) P (A) 0.75 , P (B) 0.5 , P (A and B) _____ ANSWER 0.75 x 0.5 = 0.375

15. Daily Homework Quiz For use after Lesson 12. 8 1. Events A and B are dependent. P(A & B) = P(A) x P(B) P (A) 0.75 , P (B given A) _?_ , P (A and B) 0.3 ANSWER 0.3 ÷ 0.75 = 0.4

17. Lesson 12.8 , For use with pages 694-700 2. You choose an M or P. 1. You choose an O. You choose a card at random from a bag which contains cards with the letters in the word MONOPOLY. Find the ODDS . 1 3 = ANSWER 3 5 ANSWER 2 6

19. Dependent & Independent Events Section 12. 8

21. EXAMPLE 3 Finding Probability of Dependent Events Bingo SOLUTION You need B 7 and N 44 for bingo. Find the probability of success when each of the next 2 numbers is drawn. Then multiply. You are playing the bingo card shown. The caller has 50 numbers left to call. What is the probability that you will get bingo with the next 2 numbers called?

22. EXAMPLE 3 Finding Probability of Dependent Events P ( B 7 or N 44) There are 50 numbers left to call. Multiply the probabilities. There are 49 numbers left to call. = 1 25 P ( remaining number ) = 1 49 P ( both numbers ) = 1 25 1 49 = 1225 1 ANSWER The probability that you will get bingo when the next 2 numbers are called is, or about 0.0008 . 1225 1 2 50 =