The probability of team B winning the match in this scenario is c) 1/2.
How can you solve the probability of B winning the match?
Both teams have scored the same number of goals, so the match is tied.
The winner is decided by a die roll, where the first captain to get a six wins.
Since Captain A throws first, there are two possibilities:
Team A wins on their first throw: This happens if Captain A throws a six on the first roll. The probability of this is 1/6.
Team B wins on one of their throws: If Captain A doesn't get a six on the first try, Captain B has the chance to win on any of their remaining throws. The probability of this happening depends on how many throws Captain A takes before getting a six.
Therefore, the total probability of B winning the match (considering all possible scenarios where A doesn't win on the first throw) is:
1/6 * (1 + 1/6 + 1/18 + ...)
This is an infinite geometric series with a first term of 1/6 and a common ratio of 1/6. The sum of this series is:
1/6 / (1 - 1/6) = 1/2
Therefore, the overall probability of B winning the match is:
Team B wins on first throw + Team B wins on any subsequent throw
= 1/6 + 1/2
= 3/6
= 1/2