# Dependent Events Objective: Find the probability of dependent events. Standard Addressed: 2.7.11: D Use theoretical probability distributions to make judgments.

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Dependent Events Objective: Find the probability of dependent events. Standard Addressed: 2.7.11: D Use theoretical probability distributions to make judgments about the likelihood of various outcomes in uncertain situations.

KNOWING THE OUTCOME OF ONE EVENT CAN AFFECT THE PROBABILITY OF ANOTHER EVENT

If one event does affect the occurrence of the other event, the events are dependent. Probability of Dependent Events Probability of Dependent Events Events A and B are dependent events if and only if P(A and B) = P (A) x P(B).

SOMETIMES THE PROBABILITY OF THE SECOND EVENT CHANGES DEPENDING ON THE OUTCOME OF THE FIRST EVENT.

Ex. 2 A bag contains 12 blue disks and 5 green disks. For each case below, find the probability of selecting a green disk on the first draw and a green disk on the second draw. a. The first disk is replaced. a. The first disk is replaced. 5/17 * 5/17 = 25/289 = 8.7% 5/17 * 5/17 = 25/289 = 8.7% b. The first disk is NOT replaced. b. The first disk is NOT replaced. 5/17 * 4/16 = 20/272 = 7.35%

Ex. 3 A bag contains 8 red disks, 9 yellow disks, and 5 blue disks. Two consecutive draws are made from the bag WITHOUT replacement of the first draw. Find the probability of each event. Ex. 3 A bag contains 8 red disks, 9 yellow disks, and 5 blue disks. Two consecutive draws are made from the bag WITHOUT replacement of the first draw. Find the probability of each event. a. red first, red second a. red first, red second 8/22 * 7/21 = 56/462 = 12.12% b. yellow first, blue second b. yellow first, blue second 9/22 * 5/21 = 45/462 = 9.7% c. blue first, blue second c. blue first, blue second 5/22 * 4/21 = 20/462 = 4.3% d. red first, blue second d. red first, blue second 8/22 * 5/21 = 40/462 = 8.7%

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