Thank you to Anna from Mt Eliza North Primary School, Australia, who sent us this solution (originally to another version of this problem):
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, by [Arsenal] scoring first and then [Chelsea] or [Chelsea] scoring first and then [Arsenal]. There is one way for the end result, 2-0, [Arsenal] gets the 2 goals without [Chelsea] getting 1. And there is only one way you can get the end result 0-2, by [Chelsea] getting both the goals. Therefore the end
result 1-1 is more likely.
3. Is this a reasonable assumption?
Yes. Even if [Arsenal] are more confident and [Chelsea] 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?
In Alison's model the team who scores first is twice as likely to score the next goal.
The chance of ending 2-0, with the teachers winning, is: