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three companies are bidding on a contract . the relative qualities of the companies are such that company A is twice as good as company B and company B is three times as good as company . what is the probability of each company winning the contract ?

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  • $\begingroup$ There's not enough information here. What process determines which company wins the contract? Why doesn't the best company always win? $\endgroup$ – Alex Becker Mar 24 '14 at 22:03
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Hint: Assuming that a how good a company is, is precisely it's probability of winning the contract (as it is mentioned in the comments), then we have that $$P(A)=2P(B)$$ and $$P(B)=3P(C)$$ and $$P(A)+P(B)+P(C)=1$$ Thus $$P(A)=2(3P(C))=6P(C)$$ which gives $$6P(C)+3P(C)+P(C)=1$$

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  • $\begingroup$ So you are assuming that how "good" a company is is precisely it's probability of winning the contract? $\endgroup$ – Alex Becker Mar 24 '14 at 22:06
  • $\begingroup$ @AlexBecker Yes, since the OP does not give much information, I had to guess. This is the simplest way. Anyway, I do not think that this post will remain open for very long... so, if you think I should delete my answer, I am ok doing it $\endgroup$ – Jimmy R. Mar 24 '14 at 22:14
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    $\begingroup$ No, not at all. But you should probably mention this assumption in the answer. $\endgroup$ – Alex Becker Mar 24 '14 at 22:17
  • $\begingroup$ @AlexBecker Ok, I did, thanks for the comment! $\endgroup$ – Jimmy R. Mar 24 '14 at 22:20
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Problem is ill-posed. What does "twice as good" mean? In the real world of aerospace subcontracting, we engineers evaluate proposals on a "goodness" scoring system that computes a weighted sum of the quality of each solicitation point. Usually the top scoring proposals are very tightly grouped, never differing by a factor of 2. So, without further clarification, this is not truly a math problem.

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