12- 8 Probability of Compound Events Objective: Find probabilities of exclusive and overlapping events and independent and dependent

12- 8 Probability of Compound Events Is the possibility of two or more events linked with the word And or the word OR.

12- 8 Probability of Compound Events Mutually exclusive: can’t happen at same time P(A or B) = P(A) + P(B) Overlapping events can happen at same time P(A or B) = P(A) + P(B) – P(A and B)

12- 8 Probability of Compound Events Spinner has 20 sections numbered 1 to 10. Probability of spinning a 2 or a 5? Can’t land on both at same time so events are exclusive. P(2 or 5) = P(2) + P(5)

12- 8 Probability of Compound Events Spinner has 20 sections numbered 1 to 10. Probability of spinning a multiple of 2 or a 5? Since a number can be a multiple of 2 and of 5, such as 10, The events are overlapping. P(Multiples of 2 or 5) = P(multi 2) + P(multi 5) – P(both) = 10 20 + 4 20 - 2 20 Simplify

12- 8 Probability of Compound Events Independent events if the occurrence of one event does not effect the other. P(A and B) = P(A) ∙ P(B)

12- 8 Probability of Compound Events Roll a red cube and a blue cube. What is probability of rolling a 3 on red and even on blue? P(3 on red) = 1 6 P(even on blue) = 3 6 = 1 2 P(both) = 1 6 ∙ 1 2 =

12- 8 Probability of Compound Events Two events are dependent if one event affects the probability of the second event. Choose and NOT replace the object. A and B are dependent events; P(A then B) = P(A) ∙ P(B after A)

12- 8 Probability of Compound Events GRIDDED RESPONSE is on tiles. Without replacing the first tile, you select a second. What is the probability that you choose a R the first selection and a D the second. P(R then D) = P(R) ∙ P(D after R) = 2 15 ∙ 3 14 =

12- 8 Probability of Compound Events GRIDDED RESPONSE is on tiles. Without replacing the first tile, you select a second. What is the probability that you choose a D the first selection and a D the second. P(D then D) = P(D) ∙ P(D after R) = 3 15 ∙ 2 14 =

12- 8 Probability of Compound Events HW p. 780 9 - 27 Every third