Permutations
A permutation is an ordered arrangement
The number of permutations for n objects is n!
n! = n*(n-1)*(n-2).3*2*1
The number of permutations of n objects taken r at a time is
You hand your friend a list of your 6 favorite movies and ask her to

A Summary of Probability Rules
o P(A and B) = P(A) * P(B|A)
o P(A and B) = P(B) * P(A|B)
o P(A) = P(A and B)/P(B|A)
o P(B|A) = P(A and B)/P(A)
o P(A or B) = P(A) + P(B) - P(A and B)
o P(A) + P(not A) = 1
o P(A) = 1 - P(not A)
o P(A & B & C) = P(A) * P(B)

Contingency Table
The probability of choosing a lady second depends on whether the first was choice was a
lady. These events are dependent.
Two coins are tossed. A = first coin Heads, B = second coin Heads. P(A) = , P(B|A) =
, P(B) = . These events are in

BAYES THEOREM
o Try it with a contingency table
o 2 by 2 contingency tables (events mutually exclusive and collectively exhaustive)
o I like to start with something like 1000 tires.
o 800 made in Buffalo
o 2% = 16 are blemished
o 200 made in Syracuse
o 30

Complementary Events
o The complement of event E is event E.
o E consists of all the events in the sample space that are not in event E.
GIVEN: the weather in San Diego is excellent 80% of the days. Assuming independence, if
you go to San Diego for two da

Combinations Example
If your friend needed only to give you a list of the top 4, in no particular order, How
many different lists could she give you?
6!
( 6 4 )!4!
6 * 5 * 4 * 3 * 2 *1
15
2 *1* 4 * 3 * 2 *1
6
C4
The 6 of them in order = 720 arrangements

Multiplication Rule Another Example
o In this different case the characteristics Gender and handednessare INDEPENDENT.
o In this case the characteristics (Gender and handedness) are INDEPENDENT.
Independence occurs when the occurrence of one the Probabili

The Multiplication Rule
The probability of BOTH A and B
o We write this as P(A and B) = P(A) * P(B|A) and say The Probability of A
TIMES the Probability of B GIVEN A
Find the probability someone chosen at random is a Man who is Right-handed?
Well, isnt it

Probability Example Questions
Assuming independence, if each team gets a problem to work on (Team A gets a 3-part
problem), with each member responsible for a part
o What is the probability Team A gets theirs INcorrect? 1- P(all correct) or .0297
o What i

Probability Review
We have 2 teams of students:
TEAM A, the Hotshots, consists of 3 students, each of whom gets 99% of the answers
correct.
TEAM B, the Regulars, consists of 4 students, each of whom gets 60% of the answers
correct.
o Team A is given a 3 p