Combonation of 'r' elements of a finite set S of n elements is a subset of S that contains 'r' distinct elements. The notations (n/r) and nCr are both used to denote the number of combonations of r elements selected from a set of n elements (r<n)

                                                             -

nPr

n= Total Number in set

r= Number we are selecting from set

Solution to 6P2=

6x5= 30

(n

  r)

= n!/r!(n-r)!

(10

   3)

= 10!/3!(7!)

= 10x9x8x7!/3x2x7!

=120

Permutations: order is important

Combonation: order doesn't matter

an observation of any physical occurence

Expectation= (amount to win) x (probability of winning)

The expectation of winning or achieving desired results

The property of complements says that whose sum is 1 are complementary

P(e) and P(e) (w/line over it) are complementary

P(e)= successes/total #of outcomes

P(ew/ line on top)= failures/#of outcomes

in favor of event E: sucess/# of total outcomes

opposed to event E: Failures/# of total outcomes

probability of an event given that another event F has occured= P(E/F)= lE∩Fl/ lFl

A family has 2 children: P(2boys)=1/4; Sample Space GG,GB,BB,BG

OLDER CHILD IS BOY (F); NEW Sample Space: BB, BG

Therefore; P(2Boys given older is boy)= 1/2

∩If 2 events are independent, then we can find the probability of an intersection by multiplication

- If they are n mutually exclusive and equally likely possibilities, then P(E∩F)= lE∩Fl/n

=P(ElF)xP(F)

=P(E)xP(F)

P(EorF)= P(EUF)

=P(E) + P(F) - P(E∩F)

Table organizing results

EX: rolling a die 10 times you get a 1,1,2,2,3,4,5,5,5,6

Outcome  Tally

 1         2

2         2

3       1

4     1

5    3

6    1

the mean from a frequency distribution

EX: #of children per family

Step By Step

1: Determine Mean

2: Subtract Mean from each # in set

3: Square Differences

4:Find sum of the squares of the differences

5: Divide Sum by one less than the total # of #s =Variance

6: Take the sq. rt. of the Variance= Stnd. Dev.

mean-3Std.dev= .1% m-2std.dev=2,2% m-1std.dev.= 13.6% m-1std.dev. 34.1%, same %s on the opposing half

Z score

base 10

First Law (Additive): The log of the product of 2 numbers is the sum of the logs of those numbers

Second Law (subtractive): The log of the quotient of 2 numbers is the log of the numerator minus the log of the denominator

Third Law (Multiplication): the log of the pth power of a number is p times the log of that number

FV: Continuous Compounding

Present Value Formula

P: Amount to be financed (PV)

r:addon interest rate

t: time yrs to repay loan

I: amount of interest

A: Amount to be repaid (FV)

m: amount of the monthly payment

N:Number of payment

rate paid on a loan when that rate is based on the actual amount owed for the length of time that it is owed. It can be found for an add-on interest rate, r,w/ N payments by using the formula.

APR= 2Nr/N+1

Interest is calculated on the previous month's balance

P: previous balance

r: annual rate

t: 1/12

Interest calculated on the previous month's balance less credits and payments

P: adjusted ablance

r: annual rate

t: 1/12

Add outstanding balances for each day in the billing period to find what is called the average daily balance.

P: ave. daily balance

r:annual rate

t: days in billing period/ 365

A=m[(1+r/n)^nt-1]/(r/n)

process of paying off a debt by systematically making partial payments until the debt and the interest are repaid

m= P(r/n)/(1-(1+r/n)^-nt

Borda Count