PROBABILITY CALCULATIONS

It is easiest to learn how to calculate simple probabilities by using examples. We will use dice for our examples.

Example 1: What is the probability of rolling a one with a single die?

A die has six faces on it, with each face having from one to six dots. Thus, the probability of rolling a one is 1 out of 6, or 1/6. The same is true with the remaining five numbers. That is, the probability of rolling a two (or a three, or a four, or a five, or a six) is 1/6.

In general, the probability of a particular event is:

the number of instances of that particular event divided by the total number of all events

Example 2: If we rolled two dice, what is the probability of rolling a two and a six (for a total of eight)?

The probability of rolling a two with one of the dice is 1/6 and the probability of rolling a six with the other dice also is 1/6. The probability of rolling the two together is:

1/6 * 1/6 = 1/36

In general, the probability of joint occurrence of two independent events is:

the probability of the first event multiplied by the probability of the second event

Example 3: With a single die, what is the probability of rolling either a one or a three?

The probability of rolling a one is 1/6, and the probability of rolling a three is 1/6. The probability of rolling either a one or a three is:

1/6 + 1/6 = 2/6 = 1/3

In general, the probability of the occurrence of either one or the other of two independent events is:

the probability of the first event plus the probability of the second event

For more information on calculating simple probabilities, go to this book chapter and click on "Probability Calculations" in the Table of Contents. On this page, you also can do on-line experiments in which you flip a coin, roll a die, and choose cards from a deck, in order to get an intuitive "feel" for the probabilities of these events.