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# Rules of Probability Calculation

Here I summarise the rules of probability calculus. They have been stated above; here they are grouped together, so they can be found easily.
1. Probability is a number between 0 and 1:
2. If the outcome is certain, the probability of that outcome is 1: If is the probability for the variable , if and only if takes the value .
3. Definition of conditional probability: The conditional probability is defined by this formula

4. The probability that a variable takes one of a set of mutually exclusive outcomes is the sum of the probability of the outcomes: if can take no more than one of the values .
5. The probability of independent events is computed by multiplying the probability of each event: if taking the value does not depend whether or not takes the value .
6. Bayes Rule:

7. Bayes Rule (alternative form):

8. Distribution of a single variable from the joint distribution: One can find the distribution for from the joint distribution of and by summing over all values of ,

The single distribution determined from the joint is called the marginal distribution; this process is called marginalisation. Note: It is not possible to infer the joint distribution from the marginals.

Next: What is the Meaning Up: A Primer on Probability Previous: Conditional Probabilities are of
Jon Shapiro
1999-09-23