Final answer:
The probability of a playoff between two teams going to the full five games is found by calculating the number of ways both teams can win two of the first four games. There are 6 possible sequences for a 2-2 tie out of 16 total possible outcomes, leading to a probability of 6/16.
Step-by-step explanation:
The question asks about the probability of a playoff between two teams requiring the maximum number of games (five) to be decided. To determine this probability, we need to assume that each game is independent and that the series continues until one team wins three games, since that would be the minimum number of victories required to win in a best-of-five series.
For the playoff to go to a full five games, the first four games must result in a 2-2 tie between the teams, with each team winning exactly two games. The outcomes of the first four games can be win or lose, and the fifth game must be played. The exact sequence of wins and losses in the first four games is not important, only that both teams win an equal number of games (two each). The fifth game's outcome does not affect whether it is played since it will be necessary regardless of which team is projected to win.
The total number of possible ways for both teams to win two of the first four games is combinatory, following a pattern similar to binomial distribution. There are 6 possible sequences for this to occur (WWLL, WLWL, WLLW, LWWL, LWLW, LLWW). Each game has two outcomes, meaning there are 2^4, or 16, possible outcomes over the course of the first four games. Thus, the probability of the playoff going to five games is the number of sequences that result in a 2-2 tie (6) divided by the total number of possible sequences (16).