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).

Don’t use percentage numbers (0 to 100) in probability formulas.

Even though these rules of probabilities may seem simple when presented here, applying them

together in complex situations — as is done in statistics — can get tricky in practice. Here are

descriptions of the not rule, the and rule, and the or rule.

The not rule: The probability of some event X not occurring is 1 minus the probability of X

occurring, which can be expressed in an equation like this:

So if the probability of rain tomorrow is 0.7, then the probability of no rain tomorrow is 1 – 0.7, or

0.3.

The and rule: For two independent events, X and Y, the probability of event X and event Y both

occurring is equal to the product of the probability of each of the two events occurring

independently. Expressed as an equation, the and rule looks like this:

As an example of the and rule, imagine that you flip a fair coin and then draw a card from a deck.

What’s the probability of getting heads on the coin flip and also drawing the ace of spades? The

probability of getting heads in a fair coin flip is 1/2, and the probability of drawing the ace of

spades from a deck of cards is 1/52. Therefore, the probability of having both of these events

occur is 1/2 multiplied by 1/52, which is 1/104, or approximately 0.0096 (which is — as you can

see — very unlikely).

The or rule: For two independent events, X and Y, the probability of X or Y (or both) occurring is