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