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(a) Find P(A1 U A2 U A3) (b) Show that P(A1 U A2 U A3) = 1-(1-1/3)^3

(a) Find P(A1 U A2 U A3) (b) Show that P(A1 U A2 U 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 six-sided die 3 times.  Let A1 = {1 or 2 on the first roll}, A2 = {3 or 4 on the secong roll}, A3 = {5 or 6 on the third roll}.

It is given that:

P(Ai)=1/3, i = 1,2,3; 

P(Ai intersect Aj) = (1/3)^2

i does not equal j;

and P(A1 intersect A2 intersect A3) = (1/3)^3.

(a) Find P(A1 U A2 U A3)

(b) Show that P(A1 U A2 U A3) = 1-(1-1/3)^3

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