Question

Acomputer consulti 9 firm presently has bids out on thr ded project ), for , = 1, 2 3, and suppose that p A1-0.22, p Az) = 0.25, PlAg = 0.26, P A nA2-0.11, P A1 n A3 = 0.00 A(Az nAg -0.09, PiA1 probabilities given above to compute the rollowing probabilities, and-xplain in words the meaning of each one.くRound your answers to tour decimal places.) ee projects. LetA- (awar A2 nAg = 0 01. Use the Explain this probability in words. T that the firm is awarded elther project 1 or project 2 This is the probability If tha firm is awarded project1, this is the chance they wll also be awarded project 2. If the firm is awarded project 2, this is the chance they wll also be awarded project 1 This is the probability thet the firm is awarded both project 1 arid project 2 Explain this probability in words. This is the probability that the firm is awarded at least one of the projects. This is tha prohahility that the firm is awardad prajacts 1, 2, and a if the firm is ฮwarded project 1, this is the chance they will also bc awarded projects 2 and 3. the firm is awarded projects 2 and 3, this is the charice they will also be ewarded project 1. If Explain this probability in words This is tha probability that the firm is awarded projacts 1, 2, and a. If the firm is awarded project 1, this is the charice they wll also be awarded at least one of the other two projects If the firm is awarded at least onc of projects 2 and 3, this is the chance they will also be awarded project 1. O This is the probability that the firrm is awarded at least one of the projects. Explain this probability in words. This the probabity that the firm is awarded projects 1, 2, and 3. if the firm is awฮrded at least two of the projects, this is the chance that they will be awarded all three projects. This is the probabiity that the firm is ewarded at least one of the projects. If the firm is awarded at least one of the projects, this is the chance that they will be awarded all three projects.

Answer 1

please revert if P(A3)=0.28 and P(A1 n A3) =0.08 ; are different values as from picture it is not clear

b)

P(A2 n A3|A1)=P(A1 n A2 n A3)/P(A1)=0.01/0.22 =0.0455

c)

P(A2 u A3 |A1)=(P( A1 n A2)+P(A1 n A3)-P(A1 n A2 n A3))/P(A1)=(0.11+0.08-0.01)/0.22=0.8182

d)

at least one =P(A1UA2UA3)=

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

=

0.46

hence P(A1 n A2 nA 3|A1 uA2 u A3)=0.01/0.46 =0.0217