Classify each pair of events as dependent or independent. Probability of Multiple Events LESSON 9-7 Additional Examples Classify each pair of events as dependent or independent. a. Spin a spinner. Select a marble from a bag that contains marbles of different colors. Since the two events do not affect each other, they are independent. b. Select a marble from a bag that contains marbles of two colors. Put the marble aside, and select a second marble from the bag. Picking the first marble affects the possible outcome of picking the second marble. So the events are dependent.

Relate: probability of both events is probability of first event Probability of Multiple Events LESSON 9-7 Additional Examples A box contains 20 red marbles and 30 blue marbles. A second box contains 10 white marbles and 47 black marbles. If you choose one marble from each box without looking, what is the probability that you get a blue marble and a black marble? 30 50 47 57 Relate:  probability of both events is probability of first event times probability of second event Define: Event A = first marble is blue. Then P(A) = Event B = second marble is black. Then P(B) = Write: P(A and B) = P(A) • P(B)

P(A and B) = • = Multiply. = Simplify. Probability of Multiple Events LESSON 9-7 Additional Examples (continued) P(A and B) = • 30 50 47 57 1410 2850 = Multiply. = Simplify. 47 95 The probability that a blue and a black marble will be drawn is , or 49%. 47 95

Mutually Exclusive Formulas Probability of (A or B) Mutually Exclusive means that it is not possible for two events to happen at the same time. If A and B are mutually exclusive events, then P (A or B)= P(A) + P(B) If A and B are not mutually exclusive events, then P(A or B) = P(A) + P(B) – P(A and B)

Are the events mutually exclusive? Explain. Probability of Multiple Events LESSON 9-7 Additional Examples Are the events mutually exclusive? Explain. a. rolling an even number and rolling a number greater than 5 on a number cube By rolling a 6, you can roll an even number and a number greater than 5 at the same time. So the events are not mutually exclusive. b. rolling a prime number or a multiple of 6 on a number cube Since 6 is the only multiple of 6 you can roll at a time and it is not a prime number, the events are mutually exclusive.

What is the probability that a customer will choose beans or spinach? Probability of Multiple Events LESSON 9-7 Additional Examples At a restaurant, customers get to choose one of four vegetables with any main course. About 33% of the customers choose green beans, and about 28% choose spinach. What is the probability that a customer will choose beans or spinach? Since a customer cannot not choose both beans and spinach, the events are mutually exclusive. P(beans or spinach) = P(beans) + P(spinach)   Use the P(A or B) formula for mutually exclusive events. = 0.33 + 0.28 = 0.61 The probability that a customer will choose beans or spinach is about 0.61 or about 61%.

P(multiple of 2 or 3) = P (multiple of 2) + Probability of Multiple Events LESSON 9-7 Additional Examples A spinner has twenty equal-size sections numbered from 1 to 20. If you spin the spinner, what is the probability that the number you spin will be a multiple of 2 or a multiple of 3? P(multiple of 2 or 3) = P (multiple of 2) + P (multiple of 3) – P (multiple of 2 and 3) = + – 10 20 6 3 = 13 20 The probability of spinning a multiple of 2 or 3 is . 13 20