## Cimt University of Exeter Unit 5 Probability

### Background and Preparatory Work

The origins of probability are not entirely clear, but we do know of discussions between Pascal and his friend, the Chevalier de Méré, in which, for example, they considered the problem,

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*Are you more likely to obtain one six in 4 tosses of one fair die than to obtain at least one double six in 24 tosses of two fair dice*?”Some of these types of problems were published by Huygan in 1657 in his little tract ‘On reasoning in Games of Dice’. Other famous mathematicians had considered similar problems; for example, Galileo considered the problem.

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*Are you more likely to obtain a total of 9 when three fair dice are tossed than a total of 10*?” and Pepys asked Norton.“

*Which is more likely – one 6 when six dice are tossed or two 6s when 12 dice are tossed*?”These types of problems led to the Binomial distribution for probabilities, which includes the well known Pascal’s triangle of coefficients, but this is beyond the scope of this Unit. For preparatory work, make sure that you have an adequate supply of dice, spinners and coins – specialist suppliers can provide biased dice which can be used in experiments to find actual probabilities.