. Let A1 denote the event that no red balls are selected, let A2 denote the event that no white balls are selected, and let Az denote the event that no blue balls are selected. We must determine the value of Pr(A1 U A2 U A3). We shall apply Theorem 1.10.1. The event A1 will occur if and only if all ten selected balls are white or blue. Since there is probability 0.8 that any given selected ball will be white or blue, we have Pr(A1) = (0.8)10. Similarly, Pr(A2) = (0.7)10 and Pr(A3) = (0.5)10. The event A1NA2 will occur if and only if all ten selected balls are blue. Therefore Pr(A1 N A2) = (0.5)10. Similarly, Pr(A2N A3) = (0.2)10 and Pr(A1n A3) = (0.3)10. Finally, the event A0AN A3 cannot possibly occur, so Pr(A1 N A2 N A3) = 0. So, the desired probability is %3D

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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. Let A1 denote the event that no red balls are selected, let A2 denote the event that no white balls are
selected, and let A3 denote the event that no blue balls are selected. We must determine the value
of Pr(A1 U A2 U A3). We shall apply Theorem 1.10.1. The event A1 will occur if and only if all ten
selected balls are white or blue. Since there is probability 0.8 that any given selected ball will be white
or blue, we have Pr(A1) = (0.8)10. Similarly, Pr(A2) = (0.7)10 and Pr(A3) = (0.5)10. The event A1ÑA2
will occur if and only if all ten selected balls are blue. Therefore Pr(A1 N A2) = (0.5)10. Similarly,
Pr(A2N A3) = (0.2)10 and Pr(A1N A3) = (0.3)10. Finally, the event A10 ANA3 cannot possibly occur,
so Pr(A1 N A2 N A3) = 0. So, the desired probability is
Transcribed Image Text:. Let A1 denote the event that no red balls are selected, let A2 denote the event that no white balls are selected, and let A3 denote the event that no blue balls are selected. We must determine the value of Pr(A1 U A2 U A3). We shall apply Theorem 1.10.1. The event A1 will occur if and only if all ten selected balls are white or blue. Since there is probability 0.8 that any given selected ball will be white or blue, we have Pr(A1) = (0.8)10. Similarly, Pr(A2) = (0.7)10 and Pr(A3) = (0.5)10. The event A1ÑA2 will occur if and only if all ten selected balls are blue. Therefore Pr(A1 N A2) = (0.5)10. Similarly, Pr(A2N A3) = (0.2)10 and Pr(A1N A3) = (0.3)10. Finally, the event A10 ANA3 cannot possibly occur, so Pr(A1 N A2 N A3) = 0. So, the desired probability is
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