63. DICE AND PROBABILITY

On a standard die the faces have dots to the values of 1, 2, 3, 4, 5 and 6. Opposite faces add to the common number 7. You should be able to prove that this number must occur without even looking at a die! The probability of a given number coming up is obviously 1/6 – the same for each of the face values. If we throw a pair of dice, the possible totals are 2, 3, ... , 12. However the probabilities of these numbers occurring vary. For example, 2 occurs with probability 1/12; 5 occurs with probability 4/12 or 1/3. If we construct a graph of these probablities we obtain a simplified version of the so-called normal (or bell) curve.