Marco83 wrote:

Two equally skilled teams play a four games tournament. What is the probability of the tournament ending at the fourth game with a winner?

[bonus question: how about a 40 games tournament ending on the 40th game with a winner?]

First, we have to determine what we're looking for. If we are looking for a probability that after playing 4 games there will be a winner than we must consider a case of a tie. The statement does not tell us that the teams should either win or lose. It implies there might be ties.

Therefore:

1) The total possible options are WLT: 3*3*3*3=81

2) In order to be a winner, a team can do 4W, 3W+L&T, 2W+L+T, 2W+2T, 1W+3T

a)4W=1

b)3W=4!/3!=4 and we have T or L as options=4*2=8

c)2W+L+T=4!/2!=12

d)2W+2T=4!/2!*2!=6

e)1W+3T=4!/3!=4

3)Total for one team to become a winner is 1+8+12+6+4=31

4)Total for any of two to become a winner is 31*2=62

5)The probability is 62/81