[Probability] Probability - Part 1

 

Probability

Probability - Part 1

 

Definitions

Sample Space : the set of all possible outcome of a statistical experiment 

Event : a subset of a sample space

Comlement : an event A with respect to S is the subset of all elements of S that are not in A

Intersection : the event contating all elements that are common to A and B

Pemutation : an arrangement of all or part of a set of objects.

 

Theorem 

The number of permutations of n distinct objects taken r at the same time :

 

 

 

 

The number of permutations of n distinct objects arranged in a circle : (n-1)!

 

The number of distinct permutations of n things of which of n1 are of one kind, n2 of a second kind, ...,nk of a kth kind :

 

 

 

 

The number of wats of partitiioning a set of n objects into r cells with n1 elements in the first cell,n2 elements in the second, and so forth, is

 

 

 

 

 

The number of combinations of n distinct objects taken r at a time :

 

 

 

 

 

if A1, A2, A3... is a sequence of mutually exclusive events, then 

P(A1 ∪A2 ∪A3 ∪···)=P(A1)+P(A2)+P(A3)+···.