Probability and Spontaneous Change

Probability = I — I, where N is the number of dice being thrown 

We should note that this relationship applies for the case at hand, but it is not general. The factor of 1 in the numerator is present because we are looking for a single specific roll (of a number four) on each die and the six in the denominator is there because there are six possible rolls for each die. With this relationship, however, we could easily predict that the chances of rolling the same number with five dice in one roll are one in 1296. (Note that the chances of rolling a specified number on all five dice—say all fours—are 1 in 7776. But if we do not specify in advance which of the six possible numbers we want on all five dice, then there will be six possible outcomes instead of just one.) Our experience with rolling dice is that we expect to have some random assortment of numbers present when five dice are rolled. Why There are very many ways to obtain a random roll. Such a roll occurs far more often precisely because it is more probable. 

Our development of the mathematics of probability bas two important features. First, it shows that to obtain the probability of a collection of events based on the probability of an individual event we must multiply. Tbis observation becomes important wben we consider just how many molecules are involved when we observe something in nature or in the laboratory. Second, the number of ways to 

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