# A PRIORI PROBABILITY

When people make probability claims, we have a right to ask why they assign the probability they do. In Chapter 8, we saw how statistical procedures can be used for establishing probability claims. Here we will examine the so-called a priori approach to probabilities. A simple example will bring out the differences between these two approaches. We might wonder what the probability is of drawing an ace from a standard deck of fifty-two cards. Using the procedure discussed in Chapter 8, we could make a great many random draws from the deck (replacing the card each time) and then form a statistical generalization concerning the results. We would discover that an ace tends to come up roughly one-thirteenth of the time. From this we could draw the conclusion that the chance of drawing an ace is one in thirteen.

But we do not have to go to all this trouble. We can assume that each of the fifty-two cards has an equal chance of being selected. Given this assumption, an obvious line of reasoning runs as follows: There are four aces in a standard fifty-two-card deck, so the probability of selecting one randomly is four in fifty-two. That reduces to one chance in thirteen. Here the set of favorable outcomes is a subset of the total number of equally likely outcomes, and to compute the probability that the favorable outcome will occur, we merely divide the number of favorable outcomes by the total number of possible outcomes. This fraction gives us the probability that the event will occur on a random draw. Since all outcomes here are equally likely,

Probability of drawing an ace = = =

Notice that in coming to our conclusion that there is one chance in thirteen of randomly drawing an ace from a fifty-two-card deck, we used only math- ematical reasoning. This illustrates the a priori approach to probabilities. It is called the a priori approach because we arrive at the result simply by reason- ing about the circumstances.