Two teams are playing a best-of-7 tournament. Each team has a 50% chance of winning. What is the probability that they reach the 7th game?
My initial thought would be that it is the probability of no teams win 4 games out of 6 games, so I calculated: $$1 - \binom{6}{4}0.5^40.5^6$$
Can someone point out what is wrong with my logic?
To reach the 7th game the score must be 3-3 after 6 games.
If a = event: player A wins a game and
b = event: player B wins a game then
one possibility is: aaabbb that is A wins first 3 games and B wins next 3 games.
P(aaabbb) = 0.5^6
Next, work out how many permutations there are of the 6 letters aaabbb. Answer is 6!/(3!3!)
Now multiply 0.5^6 and 6!/(3!3!) which gives answer 5/16