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.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...
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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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