Applied statistics/Tutorials: Difference between revisions
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===The addition rule=== | ===The addition rule=== | ||
For two mutually exclusive events, A and B,<br> | |||
:::P(A or B) = P(A) + P(B) | the probability that either A or B will occur is equal to the probability that A will occur plus the probability that B will occur,<br> | ||
:::P(A or B) = P(A) + P(B). | |||
===The multiplication rule=== | ===The multiplication rule=== | ||
For two independent (unrelated) events, A and B,<br> | |||
the probability that A and B will both occur is equal to the probability that A will occur multiplied by the probability that B will occur,<br> | |||
:::P(A and B) = P(A) x P(B) | :::P(A and B) = P(A) x P(B) | ||
===Bayes' theorem=== | ===Bayes' theorem=== | ||
:::P(A/B) = P(B/A) x P(A)/P(B) | The probability that event A will occur, given that event B has occurred is equal to the probability that B will occur, given that A has occurred, mutiplied by the probability that A will occur divided by the probability that B will occur,<br> | ||
:::P(A/B) = P(B/A) x P(A)/P(B). | |||
Revision as of 03:01, 29 June 2009
Rules of chance
The addition rule
For two mutually exclusive events, A and B,
the probability that either A or B will occur is equal to the probability that A will occur plus the probability that B will occur,
- P(A or B) = P(A) + P(B).
The multiplication rule
For two independent (unrelated) events, A and B,
the probability that A and B will both occur is equal to the probability that A will occur multiplied by the probability that B will occur,
- P(A and B) = P(A) x P(B)
Bayes' theorem
The probability that event A will occur, given that event B has occurred is equal to the probability that B will occur, given that A has occurred, mutiplied by the probability that A will occur divided by the probability that B will occur,
- P(A/B) = P(B/A) x P(A)/P(B).