If A and B are dependent events,

If A and B are independent events,

]]>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.

]]>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