8. , \'8 4. points DevorcSsars 2 E03 A computer consulting firm pos ntly has bid

Question

8. , '8 4. points DevorcSsars 2 E03 A computer consulting firm pos ntly has bids out on three p ects. Let A-lawarded pro ca ri-1, 2, 3 and suppose that P Ai)s 0.22 RA2)-0 26, P A)-0.29 PLA n Az) = 0.08, PAL n A3)-0.09 p(A2 n A3) n 2 n Mg)-0.01. Use the probabilites grven above to compute the following probabilities, and explain in words the meaning of each one. Round your answers to four decimal places.) My Notes Ask Your Teacher 0.07 A 4 Explain this probability in words. lf the fimm is awarded proiect 2, this 15 the chance they will also be awarded proiect 1. f the fim is awarded project 1, this is the chance they ill also be awarded project 2 This is the probability that the firm is awarded either project 1 or project 2. This is the probability that the firm is awarded bath project 1 and pruject 2. Explain this probebility in words. This is the pillability that the firm is nearded at least crie tif the p'njrrts. This is the probability that the firm is awarded projects 1, 2, and 3. If the firm is awarded projects 2 and 3, this is the chance they will also bc wandcd project 1. If the firm is awarded proiect 1, this is the chance they will also be awarded prolects 2 and 3. Exclain this probability in words T the tim is awarded projert 1, this is the chance they will also be awarded at least one of the ather two projects. If the firm is awarded t least one of projects 2 and 3, this is the chance they will also bc awarded projcct 1 This is the probability that the firm is awarded at least one of the proects. 1 his 1s the probability that the firm is awarded projects 1,2, and 3. Explain this probability in words. This is the 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. tf the firrn is awarded it least one a the projets, this is; the charicte that they will bet Wardmd all three projets, If the firm is awarded at least two of the projects, this is the chance that they will be awarded all three projects

Explanation / Answer

(a) Here writing question mathematically,

Pr(A2U A1) = Pr(A1) + Pr(A2) -  Pr(A1 A2)

Pr(A2U A1) = 0.22 + 0.26 - 0.08

Pr(A2U A1) = 0.4

Pr(A2 l A1) = Pr(A2 A1)/Pr(A1) = 0.08/0.22 = 0.3636

Option B is correct regarding the explaintion of the said term.

(b) Pr(A2 A3 l A1) = Pr(A2 A3 A1)/ Pr(A1) = 0.01/0.22 =  0.04545

Option D is correct regarding the explaination of the said term.

(c) Pr(A2U A3 l A1) = Pr[(A2U A3) A1] /Pr(A1) = [Pr(A1 A2) +Pr(A1 A3) - Pr(A1 A2 A3 )]Pr(A1)

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

Option A is correct regarding the explaination of the said term.

(d) Pr(A1 A2 A3 l A1 U A2 U A3) = Pr(A1 A2 A3)/ Pr(A1 U A2 U A3)

Pr(A1 U A2 U A3) = Pr(A1) + Pr(A2) + Pr(A3) - [Pr(A1 A2) +Pr(A1 A3) + Pr(A2 A3)] - 2 Pr(A1 A2 A3)

= (0.22 + 0.26 + 0.29) - (0.08 + 0.09 + 0.07) - 2 * 0.01 = 0.51

Pr(A1 A2 A3 l A1 U A2 U A3) = Pr(A1 A2 A3)/ Pr(A1 U A2 U A3) = 0.01/0.51 = 0.0196

Here option C is correct about the said probability that means if they are awarded at least one project, the given probability is that they will be provided with all projects.

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