# Section 13-1

# Probability and Odds

Probability is a measure of how likely something is to happen. It is expressed with a number between 0 and 1; 0 means "impossible" and 1 means "certain".

For example: suppose I ask you to randomly choose a letter of the alphabet between J and N, inclusive. The possibilities are J, K, L, M, N. The probability that you pick a vowel is 0. The probability that you pick a consonant is 1. The probability that you pick K is 1/5 = 0.2.

In general, the probability that an event occurs is given by:

Example:

Suppose you roll a six-sided die. Find the probability that you roll a number greater than four.

There are six possible outcomes: 1, 2, 3, 4, 5 and 6. There are two favorable outcomes: 5 and 6. So the probability is:

## ODDS

Sometimes, probabilities are stated in terms of odds.

In the example above, there are two favorable outcomes (5 and 6), and four unfavorable outcomes (1, 2, 3, 4). So the odds are

,

or "one-to-two" that you will roll a number greater than four.