two teams meet in playoff series at the end of the regular season. Team A won 55 of 81 games played in its home stadium during the regular season, while Team B won 48 of 81 games played in its home staduim. The first two games of the series will be played in Team A's home stadium the next two games in Tean B's home stadium. In the adsence of any other information, which expression is equal to the probability that Team A will win the first four games in a row?
(55/81)(55/81)(33/81)(33/81)
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To find the probability that Team A will win the first four games in a row, we need to consider the probabilities of each individual game outcome and multiply them together.
The probability of Team A winning a game in their home stadium is given as 55/81, which means they won 55 out of 81 games.
The probability of Team B winning a game in their home stadium is given as 48/81, which means they won 48 out of 81 games.
Since the first two games of the series are played in Team A's home stadium and the next two games are played in Team B's home stadium, we have two cases to consider:
Case 1: Team A wins both games in their home stadium (probabilities multiply):
(55/81) * (55/81)
Case 2: Team B wins both games in their home stadium (probabilities multiply):
(48/81) * (48/81)
Finally, to get the probability that Team A wins the first four games in a row, we add the probabilities from both cases:
(55/81) * (55/81) + (48/81) * (48/81)
Note: Without any additional information about the teams' performance or the playoffs format, we assume that each team's home stadium advantage remains the same in the playoffs.