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1. What are the possible results if 2 goals are scored in total?
2-0, 0-2, 1-1
2. Why are they not all equally likely?
They are not all equally likely because there are two ways you can get the end result, 1-1. There is one way for the end result, 2-0, the teachers get the 2 goals without the students getting 1. There are 2 ways you can get the end result 1-1, by the teachers scoring then the students or the students scoring then the teachers. And there is only one way you can get the end result 0-2, by the students getting both the goals. Therefore the end result 1-1 is more likely.
3. Is this a reasonable assumption?
Yes. Even if The Teachers are more confident and The Students are trying harder, those equal out so the chance would stay at 50-50.
4. What are the probabilities of each result according to Alison's model?
To get the end result, 2-0, with the teachers winning. There would be a 33.3% (1/2 x 2/3 = 1/3 converted into a percentage) chance of that occurring. And the opposite for the end result 0-2. But when the end result 1-1 appears twice you multiply by the half (1/2 x 1/3 = 1/6) then add both 1/6’s together (1/6 + 1/6 = 1/3) and convert it into a percentage you will end up with 33.3%. Therefore, using Alison’s model (the team who scores first is twice as likely to score the next goal) there is a 33.3% chance of any result occurring.
5. What are the probabilities of each result according to Charlie’s model?
Charlie’s model shows that it is more likely to end up with the result 1-1. This is because he suggests that if one team gets the first goal, the other team will get the second which will have an end result of 1-1. There is a 16.5% chance to have the end result of 2-0, a 16.5% chance of the end result being 0-2 and a 66.6% to have the end result being 1-1.