9-11 State Maths Paper 2021. docx



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9-11 State Maths Paper 2021

QUESTION THREE (4 MARKS)
There are 64 teams who play single elimination tournament, hence 6 rounds, and you have to predict all the winners in all 63 games. Your score is then computed as follows 32 points for correctly predicting the final winner, 16 points for each correct finalist, and soon, down to
1 point for every correctly predicted winner for the first round. (The maximum number of points you can get is thus 192.) Knowing nothing about any team, you flip fair coins to decide everyone of your 63 bets. Compute the expected number of points.


Task developed by Giacomo Rotolo-Ross, University of Sydney, 2020
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