Consider a random experiment of selecting a ball from an urn contain- ing four balls numbered 1, 2, 3, 4. Suppose that all the four outcomes are assumed equally likely. Let A = {1, 2}, B = {1, 3}, and C = {1, 4} be the events. Prove that these events are pairwise independent but not mutually independent.
Consider a random experiment of selecting a ball from an urn contain- ing four balls numbered 1, 2, 3, 4. Suppose that all the four outcomes are assumed equally likely. Let A = {1, 2}, B = {1, 3}, and C = {1, 4} be the events. Prove that these events are pairwise independent but not mutually independent.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CT: Chapter Test
Problem 30CT: In a batch of 20 tires, 2 are known to be defective. If 4 tires are chosen at random, find the...
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Transcribed Image Text:Consider a random experiment of selecting a ball from an urn contain-
ing four balls numbered 1, 2, 3, 4. Suppose that all the four outcomes are assumed
equally likely. Let A = {1, 2}, B = {1, 3}, and C = {1, 4} be the events. Prove that
these events are pairwise independent but not mutually independent.
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