The Language of Argument

2 4 5

a P r i o r i P r o b a b i l i t y

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 rea-

soning about the circumstances.

In calculating the probability of drawing an ace from a fifty-two-card

deck, we took the ratio of favorable equally likely outcomes to total

equally likely outcomes. Generally, then, the probability of a hypothesis h,

symbolized “Pr(h),” when all outcomes are equally likely, is expressed as

follows:

Pr 1 h 25

favorable outcomes

total outcomes

We can illustrate this principle with a slightly more complicated example.

What is the probability of throwing an eight on the cast of two dice? The fol-

lowing table lists all of the equally likely ways in which two dice can turn up

on a single cast. Notice that five of the thirty-six possible outcomes produce

an eight. Hence, the probability of throwing an eight is 5/36.

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