# Randomness and Probability

## Randomness

Major points:

- Random does not mean haphazard!
- For random events, an
**individual** outcome is uncertain.
- We can reasonably predict distributions of random events if we know their probability.

## Probability principles

These principles are also presented in section 4.2.

- A probability is a number between 0 and 1. An event with a
probability of 0 will never occur. An event with a probability
of 1 will always occur.
- For random phenomena, a sample space is the set of all possible
outcomes. Some outcome from the sample space must always occur.
- The probability that an event does not occur, is 1 minus the
probability of the event occurring.
- If two events cannot occur at the same time, then the
probability of either event occurring is the sum of their
probabilities (addition rule).
- For
**independent** events, the probability of
both events occurring is the product of their individual events
(multiplication rule).

Sometimes it's useful to create an exhaustive list of
mutually exclusive events. If each event is equally likely, we
can calculate the probability of any combination of events by
summing their number and dividing by the total number of events
(see p. 301).

Last modified: Mon Jan 31 11:01:48 Central Standard Time 2005