The Five Nations Rugby Championship. This problem concerns a rugby tournament be

Question

The Five Nations Rugby Championship. This problem concerns a rugby tournament between five nations Ireland, England, Wales, Scotland, and France. Each team plays all the other teams and each pair of teams meets only once no home and away games). game is either won lost no draws) and in every case the probability is 50% on either team winning. The question is: given that each of the five teams plays four games, what are the chances each team wins two games and loses two (the order of wins and losses doesn't matter)? Note that since Italy joined, the tournament now actually involves six nations. Hint: This is one of those problems where all the outcomes are equally likely. The hard part is computing the number of favourable outcomes.

Explanation / Answer

Since the five teams are present and the proabability of each team winning against other team is 0.5

We have the following matches

A<B<C<D<E are 5 teams

probability of above model is

= 0.5^10

= 0.0009765

If 6 teams come into picture

no of matches

6C2 = 6*5/2 = 15

prob = 0.5^15

= 3.05*10^(-5)

matches Win Prob AB A 0.5 AC A 0.5 AD D 0.5 AE E 0.5 BC B 0.5 BD B 0.5 BE E 0.5 CD C 0.5 CE C 0.5 DE D 0.5

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