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11-3 Probability of Multiple Events Warm Up! 1. How many outcomes are there for rolling a die? 2. How many outcomes are there for tossing a coin? 3. How many outcomes are there for rolling a die and then tossing a coin? 4. Does the outcome from rolling a die affect the outcome of tossing a coin? Explain. Vocabulary Compound Event – Probabilities of two or more things happening at once. Independent Events – When the outcome of one event does not affect the probability of second event, the two events are independent. Dependent Events – Two events are dependent if the occurrence of one event affects the probability of the second event. Algebra 2: Lesson 11-3 Probability of Multiple Events Page 1 Example 1: Tell whether each event is independent or dependent. a.) Earning grades on your tests and earning your final semester grade. b.) Selecting a red apple and then a green apple from a bag of 6 red and 4 green apples, if no apples are returned to the bag. c.) Selecting a red apple and then a green apple from a bag of 6 red and 4 green apples, if the first apple is returned to the bag before the next selection. d.) Flipping a coin and pulling a card from a deck of cards. Probability of Independent Events For independent events A and B: P(A and B) = P(A) P(B) Algebra 2: Lesson 11-3 Probability of Multiple Events Page 2 Example 2: Suppose you toss a coin and roll a die. Find the probability of getting heads on the coin and ‘5’ on the die. Example 3: Suppose you spin a spinner with the numbers 1, 2, 3, and 4, and pick a card from a standard deck. Find the probability of spinning a ‘4’ and choosing a face card. Example 4: A bag contains 3 red marbles and 5 blue marbles. One marble is chosen at random and then replaced. A second marble is drawn. Find P(red, then blue). Probability of Dependent Events For dependent events A then B: P(A, then B) = P(A) P(B, after A) Algebra 2: Lesson 11-3 Probability of Multiple Events Page 3 Example 5: A bag contains three red marbles and five blue marbles. One marble is chosen at random and is not replaced. A second marble is drawn. Find P(red, then blue). Example 6: There are five discs in a CD player. Disc 1 has 8 songs, disc 2 has 10 songs, disc 3 has 13 songs, disc 4 has 9 songs, and disc 5 has 10 songs. The player has a “random” button that selects songs at random and does not repeat until all songs are played. What is the probability that the first song is selected from disc 3 and then second song is selected from disc 4? Example 7: Two cards are drawn from a standard deck. The first card is not returned to the deck before the second draw. Find P(face, then face). Homework: pp. 708 – 709 =>9 – 15, 22 – 26, 31 – 34 Algebra 2: Lesson 11-3 Probability of Multiple Events Page 4