Math Is Fun Forum

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Probability Formulas

Probability Formulas

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

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,421

Re: Probability Formulas

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

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

All_Is_Number

Member

Registered: 2006-07-10

Posts: 258

Re: Probability Formulas

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.

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Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Probability Formulas

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)