[T1.2] Statistical reasoning

Representing probabilities

A probability is represented by a number between 0 and 1. An event that is certain to happen is assigned a probability of 1. An event that is certain not to happen is assigned a probability of 0. To say that an event has some value in between means that it may or may not happen; the larger the probability, the more likely the event. To be more precise about what probability actually means is surprisingly difficult; click here for a brief discussion of this topic.

Still, even if we can't say precisely what a probability is, we all know how to assign probabilities to simple events. For example, we all know that if we toss a coin, the probability of getting heads is 1/2. That's because there are two outcomes, heads and tails, and for a fair coin they have the same chance of occurring. Since the probabilities must add up to 1 (one or the other outcome is certain to happen), the probability of each outcome must be 1/2. Similarly, if you roll a six-sided die, there are six equally probable outcomes, so the probability of each outcome is 1/6.

As an abbreviation, it is customary to use a capital P to stand for probability. So, for example, we can abbreviate "The probability of getting heads when I toss this coin is 1/2" as follows:

The symbol inside the parentheses stands for the outcome in question; I've used the letter H to stand for getting heads. Unless it's obvious, you need to state the meaning of the symbol you use to stand for the outcome.