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## 'Who's the Winner?' printed from http://nrich.maths.org/

When the teachers play the students at hockey, they
are equally matched - at any point in the match, either team is
equally likely to score.

What are the possible results if 2 goals are scored in
total?

Why are they not all equally likely?

This mathematical model assumes that when a goal is scored, the
probabilities do

not change. Is this a reasonable assumption?

Alison suggests that after a team scores, they are then twice as
likely to score the next goal as well, because they are feeling
more confident. What are the probabilities of each result according
to Alison's model?

Charlie thinks that after a team scores, the opposing team are
twice as likely to score the next goal, because they start trying
harder. What are the probabilities of each result according to
Charlie's model?

The models could apply to any team sport where a small number of
goals are typically scored.

You could find some data for matches between closely matched teams
that finished with two goals and see which model fits most closely
to what happened.

You will need to make some assumptions about what it means for
teams to be "closely matched".

Send us your conclusions, and explain the reasoning behind the
assumptions you chose to make.