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Section 13-1

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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:

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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.