By Brian Bolt, David Hobbs
This publication for lecturers indicates initiatives which cater for a variety of ideas and abilities, and hyperlinks with different curriculum matters.
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A study of the mathematics of gambling might convince some pupils that the chances of winning are usually very remote. 1 Horse racing 2 Roulette wheels The Monte Carlo version of the roulette wheel has 37 sections, marked 0 to 36. You bet on any number and, if you win, you get 35 times the amount you staked and also your 11-10 Tamatour, 3-1 Guessing, 11-2 Mowsoom, Parsons Child, 10-1 Tonquin. stake is returned. 7%. If you put £1 on each horse and Tamatour won Apart from the 0, half of the sections are red would you make a profit?
I I Have football attendances declined over the years? 1 2 Have there been changes in the mean scores, variability of scores, etc. over the years? 13 What would be the effect of changing the points scheme? Before 1981 in England two points were awarded for a win and one for a draw. Subsequently three points have been given for a win, and one for a draw. A computer program could be devised to allow various points schemes to be tested. Sport 35 1 4 How good are newspapers at predicting football results?
On some scores the customer wins, on others they lose. The game can be analysed theoretically from expected frequencies by considering the 36 possible outcomes. With the scheme shown you would expect to pay out 30p on two results, 20p on four results and lOp on six results. 60 on average for every 36 customers. This does not mean that a profit is guaranteed every 36 customers, but in the long run you should win. Try the game with the pay-out scheme shown. Keep a record of the outcomes so that you can compare your results with the theoretical predictions.
101 Mathematical Projects by Brian Bolt, David Hobbs