A computer consulting firm presently has bids out on three projects. Let Aiaward

Question

A computer consulting firm presently has bids out on three projects. Let Aiawarded project 0, for i- 1, 2, 3, and suppose that PA1) = 0.22. PAo) = 0.25. P(A) = 0.28, PA n A2) = 0.09. Pa nA9 = 0.08. P(A2 n 43) = 0.07, PCA 1 n A2 nA) = 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.) Explain this probability in words If the firm is awarded project 1, this is the chance they will also be awarded project 2.If the firm is awarded project 2, this is the chance they will also be awarded project 1 the firm is awarded both project 1 and project 2.This is the probability that the firm is awarded either This is the probability that project 1 or project 2. Explain this probability in words If the firm is awarded project 1, this is the chance they will also be awarded projects 2 and 3.This is the probability that the firm is awarded at least one of the projects and 3, this is the chance they will also be awarded project 1' This is the probability that the firm is If the firm is awarded projects 2 awarded projects 1, 2, and 3 (c) P(A2 u A3 | A1) = Explain this probability in words CThis is the probability that the firm is awarded at least one of the projects. This is the probability that| If the firm is awarded at least one of projects 2 and 3, this the firm is awarded projects 1, 2, and 3. is the chance they will also be awarded project 1. If the firm is awarded project 1, this is the chance they will also be awarded at least one of the other two projects Explain this probability in words 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. probability that the firm is awarded at least one of the projects This is the probability that the firm is awarded projects 1, 2, and 3. This is the

Explanation / Answer

a) P(A2|A1) =P(A1nA2)/P(A1)=0.09/0.22 =0.4091

if the firm is awarded project 1 then this is the probability that firm will also be awarded project 2.

b)

P(A2nA3|A1) =P(A1nA2nA3)/P(A1)=0.01/0.22 =0.0455

if the firm is awarded project 1 ; this is the chance they will also be awared projects 2 and 3.

c)P(A2UA3|A1) =P((A2UA3)nA1)/P(A1) =(P(A1nA2)+P(A1nA3)-P(A1nA2nA3))/P(A1)

=(0.09+0.08-0.01)/0.22=0.7273

if the firm is awarded project 1 ;this is the chance they will also be awared at least one of  the other two projects.

d)P(A1UA2UA3)=P(A1)+P(A2)+P(A3)-P(A1nA2)-P(A1nA3)-P(A2nA3)+P(A1nA2nA3)

=0.22+0.25+0.28-0.09-0.08-0.07+0.01=0.52

P(A1nA2nA3|A1UA2UA3) = =P(A1nA2nA3)/P(A1UA2UA3)=0.01/0.52=0.0192

if the firm is awarded at least one of the projects this is the chance they will be awarded all three projects.

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