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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,631

Probability Formulas

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,812

**Probability of an event**

If the sample space, S, is discrete(i.e.n(S) is finite) then the probability p(E) of the event E is given by

i.e the number of favourable outcomes/total number of outcomes.

It should be remembered

The complementary event E' of the event E is the event of E not happening and

**Odds in favor, odds against**

The odds in favor of the event E is

The odds against the event E is

If the odds in favor of the event E is a:b, then

If the odds against the event E is a:b, then

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**All_Is_Number****Member**- Registered: 2006-07-10
- Posts: 258

**Benford's Law**

Benford's law states that the probability P that digit D appears in the first place is given by (logarithm base 10):

P = log (1 + 1/D)

Therefore, for D = 1

P = log (1 + 1/1) = log (2) = 0.301,

For D = 2

P = log (1 + 1/2) = log (1.5) = 0.176,

And so on. For D = 9

P = log (1 + 1/9) = log (1.11. . .) = 0.046

The more general law says, for example, that the probability that the first three digits are 1, 5, and 8 is:

P = log (1 + 1/158) = 0.0027

The above was copied verbatim from The Golden Ratio by Mario Livio p. 267 (C) 2002 Mario Livio ISBN: 0-7679-0816-3

This property can be useful in accounting / finance.

*You can shear a sheep many times but skin him only once.*

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**Daniel123****Member**- Registered: 2007-05-23
- Posts: 663

If A and B are not mutually exclusive (or even if they are, as P(A∩B) = 0),

If A and B are dependent events,

If A and B are independent events,

*Last edited by Daniel123 (2008-03-11 09:30:47)*

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