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Science 54
H. Dorsch (Germany)

Arts 19
M. Schilli (Germany)

53.

Mathematics and Probability

Blaise Pascal knew that snake eyes (double ones) and boxcars (double sixes) very rarely turn up in throwing a pair of dice since they have a 36-to-1 chance of turning up whereas seven has a 6-to-1 chance. He understood that it would be easier to calculate the probabilitiy of not throwing a double six. That would be 35/36. He also understood that the probability of two independent events happening is the product of the probabilities of the individual events and that , therefore, the probability of not throwing a double six on n throws is (35/35)n.
 
He calculated (35/36)24, and (35/36)25 to conclude:

1.

A slightly smaller than even chance of getting double sixes on 24 rolls of the dice.

2.

A slightly better than even chance of getting double sixes on 24 rolls of the dice.

3.

An even chance of getting double sixes on 24 rolls of the dice.

Author: Joseph Mazur

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