Daniel MeissnerNick Lauber

Kaitlyn StanglLauren Desordi

9B Probability

Binomial Theorem

Permutation

Combinations

Independent

Mutually Exclusive

Vocabulary

• (a+b)n = nC0anb0 + nC1an-1b1 + nC2an-2b2 +….nCnA0bn

The Binomial Theorem

If event E1 can occur m1 different ways and event E2 can occur m2 different ways then the number of ways they can both occur is m1 * m2

Equation for total possible outcomes:m1 * m2…. *mk

Fundamental Counting Principle

An arrangement of objects where order matters

n! = Number of permutations of n objects

nPr = Number of permutations of n objects taken r at a time

Permutations

If a set of n objects has n1 of one kind, n2 of another kind etc…

The number of distinguishable permutations

Distinguishable Permutations

!n!...n!n!n

!

k321 n

An arrangement where order does not matter

nCr: Number of combinations of n objects taken r at a time

Combinations

A happening for which the results is uncertain1. Outcomes: Possible results2. Sample Space: The set of all possible

outcomesa) Event: A subset of the sample space

Experiment

If an event E has n(E) equally likely outcomes and its sample space s has s(E) equally likely outcomes then the probability of event E is

Compliments: The probability that event E will not happen

P(E’) = 1 – P(E)

Probability

)(

)()(

Es

EnEP

Events in the same sample space that have no common outcomes:

P(A n B) = 0

If A and B are 2 events in the same sample space, then the probability of A or B is

P(A u B) = P(A) + P(B) – P(A n B)

If A & B are mutually exclusive, then just

P(A u B) = P(A) + P(B)

Two events are independent if the occurrence of one event has no effect on the occurrence of the other event

Compound Probability