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.

1. 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.
2. For random phenomena, a sample space is the set of all possible outcomes. Some outcome from the sample space must always occur.
3. The probability that an event does not occur, is 1 minus the probability of the event occurring.
4. If two events cannot occur at the same time, then the probability of either event occurring is the sum of their probabilities (addition rule).
5. 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).