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A computer consulting firm presently has bids out on three projects. Let A, = {awarded project /}, for i = 1, 2, 3, and suppose that P(A₁) = 0.23, P(A₂) = 0.26, P(A₂) · P(A₁ Ñ A₂) = 0.11, P(A₁ N A₂) = 0.05, P(A₂ MA3) = 0.08, P(A₁ N A₂ A3) = 0.01. Use the probabilities given above to compute the following probabilities, and expla words the meaning of each one. (Round your answers to four decimal places.) (a) P(A₂ A₂)=[ Explain this probability in words. O This is the probability that the firm is awarded either project 1 or project 2. O This is the probability that the firm is awarded both project 1 and project 2. O If the firm is awarded project 1, this is the chance they will also be awarded project 2. O If the firm is awarded project 2, this is the chance they will also be awarded project 1. (b) P(A₂ A₂ A₂) = [ Explain this probability in words.

A computer consulting firm presently has bids out on three projects. Let A, = {awarded project /}, for i = 1, 2, 3, and suppose that P(A₁) = 0.23, P(A₂) = 0.26, P(A₂) · P(A₁ Ñ A₂) = 0.11, P(A₁ N A₂) = 0.05, P(A₂ MA3) = 0.08, P(A₁ N A₂ A3) = 0.01. Use the probabilities given above to compute the following probabilities, and expla words the meaning of each one. (Round your answers to four decimal places.) (a) P(A₂ A₂)=[ Explain this probability in words. O This is the probability that the firm is awarded either project 1 or project 2. O This is the probability that the firm is awarded both project 1 and project 2. O If the firm is awarded project 1, this is the chance they will also be awarded project 2. O If the firm is awarded project 2, this is the chance they will also be awarded project 1. (b) P(A₂ A₂ A₂) = [ Explain this probability in words.

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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A computer consulting firm presently has bids out on three projects. Let A₁ = {awarded project /}, for i = 1, 2, 3, and suppose that P(A₂) = 0.23, P(A₂) = 0.26, P(A3) = 0.29, P(A₁A₂) = 0.11, P(A₁ A₂) = 0.05, P(A₂ A3) = 0.08, P(A₁ A₂ A3) = 0.01. Use the probabilities given above to compute the following probabilities, and explain in words the meaning of each one. (Round your answers to four decimal places.) (a) P(A₂|A₂₁) = Explain this probability in words. O This is the probability that the firm is awarded either project 1 or project 2. O This is the probability that the firm is awarded both project 1 and project 2. O If the firm is awarded project 1, this is the chance they will also be awarded project 2. O If the firm is awarded project 2, this is the chance they will also be awarded project 1. (b) P(A₂A₂A₂) = Explain this probability in words. O This is the probability that the firm is awarded at least one of the projects. O This is the probability that the firm is awarded projects 1, 2, and 3. O If the firm is awarded project 1, this is the chance they will also be awarded projects 2 and 3. O If the firm is awarded projects 2 and 3, this is the chance they will also be awarded project 1. (c) P(A₂ U A3 IA₂) = | Explain this probability in words. O This is the probability that the firm is awarded projects 1, 2, and 3. O If the firm is awarded at least one of projects 2 and 3, this is the chance they will also be awarded project 1. O If the firm is awarded project 1, this is the chance they will also be awarded at least one of the other two projects. O This is the probability that the firm is awarded at least one of the projects. (d) P(A₁ A₂ A₂ | A₁ U A₂ UA₂) = Explain this probability in words. O If the firm is awarded at least two of the projects, this is the chance that they will be awarded all three projects. If the firm is awarded at least one of the projects, this is the chance that they will be awarded all three projects. O This is the probability that the firm is awarded at least one of the projects. O This is the probability that the firm is awarded projects 1, 2, and 3.
Transcribed Image Text:A computer consulting firm presently has bids out on three projects. Let A₁ = {awarded project /}, for i = 1, 2, 3, and suppose that P(A₂) = 0.23, P(A₂) = 0.26, P(A3) = 0.29, P(A₁A₂) = 0.11, P(A₁ A₂) = 0.05, P(A₂ A3) = 0.08, P(A₁ A₂ A3) = 0.01. Use the probabilities given above to compute the following probabilities, and explain in words the meaning of each one. (Round your answers to four decimal places.) (a) P(A₂|A₂₁) = Explain this probability in words. O This is the probability that the firm is awarded either project 1 or project 2. O This is the probability that the firm is awarded both project 1 and project 2. O If the firm is awarded project 1, this is the chance they will also be awarded project 2. O If the firm is awarded project 2, this is the chance they will also be awarded project 1. (b) P(A₂A₂A₂) = Explain this probability in words. O This is the probability that the firm is awarded at least one of the projects. O This is the probability that the firm is awarded projects 1, 2, and 3. O If the firm is awarded project 1, this is the chance they will also be awarded projects 2 and 3. O If the firm is awarded projects 2 and 3, this is the chance they will also be awarded project 1. (c) P(A₂ U A3 IA₂) = | Explain this probability in words. O This is the probability that the firm is awarded projects 1, 2, and 3. O If the firm is awarded at least one of projects 2 and 3, this is the chance they will also be awarded project 1. O If the firm is awarded project 1, this is the chance they will also be awarded at least one of the other two projects. O This is the probability that the firm is awarded at least one of the projects. (d) P(A₁ A₂ A₂ | A₁ U A₂ UA₂) = Explain this probability in words. O If the firm is awarded at least two of the projects, this is the chance that they will be awarded all three projects. If the firm is awarded at least one of the projects, this is the chance that they will be awarded all three projects. O This is the probability that the firm is awarded at least one of the projects. O This is the probability that the firm is awarded projects 1, 2, and 3.
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(d)    P(A1 ∩ A2 ∩ A3 | A1 ∪ A2 ∪ A3) =  ?

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