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