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.