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Understanding the Probability of Dependent Events in Theoretical Distributions

Explore the concept of dependent events in probability theory, focusing on how the outcome of one event can influence the likelihood of another. This guide provides definitions, explanations, and worked examples involving different cases of selecting objects from bags with and without replacement. Learn to compute the probabilities of various outcomes, such as selecting disks of different colors through two consecutive draws, and grasp how theoretical probability distributions apply to real situations.

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Understanding the Probability of Dependent Events in Theoretical Distributions

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  1. 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.

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

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

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

  5. AN ADDITION TO THE NOTEPACKET:

  6. 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. 5/17 * 5/17 = 25/289 = 8.7% • b. The first disk is NOT replaced. 5/17 * 4/16 = 20/272 = 7.35%

  7. 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 8/22 * 7/21 = 56/462 = 12.12% • b. yellow first, blue second 9/22 * 5/21 = 45/462 = 9.7% • c. blue first, blue second 5/22 * 4/21 = 20/462 = 4.3% • d. red first, blue second 8/22 * 5/21 = 40/462 = 8.7%

  8. Writing Activities

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