30 PART 1 Getting Started with Biostatistics

Taking a Chance on Probability

Defining probability is hard to do without using another word that means the same

thing (or almost the same thing). Probability is the degree of certainty, the chance,

or the likelihood that an event will occur. Unfortunately, if you then try to define

chance or likelihood or certainty, you may wind up using the word probability in the

definition. No worries — we clear up the basics of probability in the following sec-

tions. We explain how to define probability as a number and provide a few simple

rules of probability. We also define odds, and compare odds to probability (because

they are not the same thing).

Thinking of probability as a number

Probability describes the relative frequency of the occurrence of a particular event,

such as getting heads on a coin flip or drawing the ace of spades from a deck of

cards. Probability is a number between 0 and 1, although in casual conversation,

you often see probabilities expressed as percentages. Probabilities are usually fol-

lowed by the word chance instead of probability. For example: If the probability of

rain is 0.7, you may hear someone say that there’s a 70 percent chance of rain.

Probabilities are numbers between 0 and 1 that can be interpreted this way:»

» ^{A probability of 0 (or 0 percent) means that the event definitely won’t occur.»}

» ^{A probability of 1 (or 100 percent) means that the event definitely will occur.»}

» ^{A probability between 0 and 1 (such as 0.7) means that — on average, over}

the long run — the event will occur some predictable part of the time (such as

70 percent of the time).

The probability of one particular event happening out of N equally likely events

that could happen is 1/N. So with a deck of 52 different cards, the probability of

drawing any one specific card (such as the ace of spades) compared to any of the

other 51 cards is 1/52.

Following a few basic rules of probabilities

Here are three basic rules, or formulas, of probabilities. We call the first one the

not rule, the second one the and rule, and the third one the or rule. In the formulas

that follow, we use Prob as an abbreviation for probability, expressed as a fraction

(between 0 and 1).