You have calculated the probability of exactly one competitor bidding correctly. I would have interpreted this question as being the probability of one or more competitor bidding, but that's just me.1. What is the probability that one other competitor will bid for the contract?
(probable answer: 0.6*0.5*0.6 + 0.4*0.5*0.6 + 0.4*0.5*0.4 =0.38)
There may be a simpler way to do this, but I did it this way:2. Assuming that all companies who bid for the contract have an equal opportunity of winning it, What is the probability that:
(a) you will win the contract?
( guessed answer:P(win)=p(loss)=0.5 let our company be Z.
p(Z win,A loss,B Loss,C Lose) +(Z w, A L, B L)*3[because instead of AB there could be BC or CA & their prob. is the same] +( Z w, A L) *3[because instead of A there could be B or C] + (Z w) =0.9375)
P(0 bidders) = .12
P(1 bidder) = .38
P(2 bidders) = .38
P(3 bidders) = .12
P(winning against 0 opponents) = 1
P(winning against 1 opponent) = .5
P(winning against 2 opponents) = 1/3
P(winning against 3 opponents) = .25
P(winning) = .12*1+.38*.5+.38*1/3 +.12*.25 = .4666...
This is indeed similar to the previous part. Try it yourself using the same method, but instead of finding the probability of there being a certain number of competitors you will need the probability that A will be competing against a certain number of competitors.(b) Competitor A wins the contract?
(is it similar to the a one above?)
0.12 is the probability of winning unopposed and .4666... is the probability of winning.(c) no other companies bid for the contract?
similar to c). find the probability of winning with one opponent and divide by probability of winning.(d)exactly one other company bid for the contract?