# Thread: De Moivre Jordan Theorem

1. ## De Moivre Jordan Theorem

Is anybody here acquainted with the De Moivre-Jordan Theorem?
Cannot locate anything on the internet, so here I shall reproduce a rather terse account of it from a textbook on Fundamental Probability:

For events $B_1, .......B_n,$ the probability that exactly m of the $B_i$ occur, m = 0, 1, . . . , n, is given by

$\sum_{i=m}^n (-1)^{i-m} {i\choose m} S_i$

An Example

Given n=4, m=2, calculate the probability that exactly 2 out of 4 $B_i$ occur is:

$P_{2,4}= {2\choose 2} S_2 - {3\choose 2} S_3 + {4\choose 2} S_4$

$
= \sum_{i

where

$\sum_{i is given by:

$P(B_1 B_2) + P(B_1 B_3) + P(B_1 B_4) + P(B_2 B_3) + P(B_2 B_4) + P(B_3 B_4)$

Looks like its something to do with the double counting like the inclusion-exclusion theory, but cannot figure it out.
Can anyone link me to the correct wiki page or try to explain to me what is happening here?

2. Ok. Think I got it. Its simply stating that there are 4 possible events which we are treating as non-disjointed, that is, they may share similar sample points.

So what is the probability that exactly any 2 such events of the 4 possible are occuring?

Using the Venn diagram to depict the 4 events where all 4 intersect each other, we can see the double-counting clearly if we just add up the 6 areas where 2 circles intersect (depicting the probability of exactly 2 events happening). This is very much like the inclusion-exclusion theory.

So, what should we call this theory? Can anyone send me more info here?