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Imagine an athletics race where there are three runners A, B and C. They all have an equal opportunity of winning. So the chances of A winning are 1 in 3.

How would I get to this answer if I only knew that the chances of A beating B is 0.5 and A beating C is 0.5 ? At first I thought that A beating B and A beating C were independent results and therefore the probability would be 0.5 * 0.5 = 0.25, but I know the answer should be 0.33

If the chances of A beating B was 0.4 and the chances of A beating C was 0.35. What is the chance of A winning the race? How do I go about working this out.

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    Why do you think that the probabilities you have are enough to work out the chance of $A$ winning in each case?2012-09-20
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    Ok, if I knew the probabilities of all permutations for all of the runners. Would I then be in a position to work out the probability of A winning? If all runners had .5 probability of beating each other. Could I work out the chance that A wins? Excuse my lack of knowledge in this area, I haven't done much probability for a while. I've read on other posts that I could perform a pairwise comparison if I know all individual probabilities. Is this correct? If I can understand how to worn out the answer j can then move on to scenarios where runners have different probabilities of beating each othe2012-09-20

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