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#1 2006-03-30 09:02:24

MathsIsFun
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Probability Formulas

Probability Formulas


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

#2 2006-04-17 01:31:30

ganesh
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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


Character is who you are when no one is looking.
 

#3 2006-07-25 01:43:36

All_Is_Number
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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.


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

#4 2008-03-12 08:30:32

Daniel123
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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 (2008-03-12 08:30:47)

 

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