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Roll a fair sided die three times. Let A1 = {1 or 2 on the first roll }, A2 = {3 or 4 on the second roll}, and A3 = {5 or 6 on the third roll}. It is given that P(Ai ) = 1/3, i = 1,2,3; P(Ai intersection Aj) = (1/3)2 , i cannot equal j; and P(A1 intersection A2 intersection A3) = (1/3)3 a) use theorem 1.1-6 to find P(A1 union A2 union A3) b) show that P(A1 union A2 union A3) = 1-(1-1/3)3

Roll a fair sided die three times. Let A1 = {1 or 2 on the first roll }, A2 = {3 or 4 on the second roll}, and A3 = {5 or 6 on the third roll}. It is given that P(Ai ) = 1/3, i = 1,2,3; P(Ai intersection Aj) = (1/3)2 , i cannot equal j; and P(A1 intersection A2 intersection A3) = (1/3)3 a) use theorem 1.1-6 to find P(A1 union A2 union A3) b) show that P(A1 union A2 union A3) = 1-(1-1/3)3

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Roll a fair sided die three times. Let A1 = {1 or 2 on the first roll }, A2 = {3 or 4 on the second roll}, and A3 = {5 or 6 on the third roll}. It is given that P(Ai ) = 1/3, i = 1,2,3; P(Ai intersection Aj) = (1/3)2 , i cannot equal j; and P(A1 intersection A2 intersection A3) = (1/3)3

a) use theorem 1.1-6 to find P(A1 union A2 union A3)

b) show that P(A1 union A2 union A3) = 1-(1-1/3)3

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