a soccer game ended in a 2-2 tie. how many different possible half-time scores were there?
To find the different possible half-time scores, we need to consider the number of goals scored by each team individually.
Let's start by considering the first team's goals. They can score a minimum of 0 goals and a maximum of 2 goals in the first half.
Case 1: The first team scores 0 goals
In this case, the second team can also score a minimum of 0 goals and a maximum of 2 goals.
Case 2: The first team scores 1 goal
In this case, the second team can also score a minimum of 0 goals and a maximum of 1 goal. (If the second team scores 2 goals, it would exceed the final score of 2-2)
Case 3: The first team scores 2 goals
In this case, the second team can only score 0 goals to maintain a final score of 2-2.
Therefore, the possible half-time scores are:
0-0
0-1
0-2
1-0
1-1
1-2
2-0
So, there are a total of 7 different possible half-time scores.