Notes on Probability Wake Forest University（笔记概率维克森林大学）.pdf

Notes on Probability Allin Cottrell 1 Probability: the classical approach The classical approach to probability, which has roots in the study of games of chance, is based on the assumption that we can identify a class of equiprobable individual outcomes of a random experiment. For example, the outcomes heads and tails are equiprobable when a fair coin is tossed; the outcomes 1, 2, 3, 4, 5, and 6 are all equiprobable when a fair die is rolled. Under these conditions the probability of any event, A, is the number of outcomes that correspond to A, which we’ll write as nA , divided by the total possible outcomes, n. In other words it’s the proportion of the total outcomes for which A occurs. nA 0 P A 1 (1) n For example, let A be the event of getting an even number when rolling a fair die. There are three outcomes corresponding to this event, namely 2, 4 and 6, out of a total of six possible outcomes, so the probability P A 3 1 . 6 2 2 Complementary probabilities This is simple but important. If the probability of some event A is P A then the probability that event A does not occur, written P A, must be P A 1 P A For example, if the chance of rain for tomorrow is 80 percent, the chance that it doesn’t rain tomorrow must be 20 percent. When trying to compute a given probability, it is sometimes much easier to compute the complementary probability first, then subtract from 1 to get the desired answer. This principle can be justified on the classical approach as follows. Let nA denote the number of outcomes that do