PROBABILITY MAP

ADDITION RULE

r

KEYWORD: ORTWO OR MORE EVENTS

MUTUALLY EXCLUSIVE

r

P(A OR B)=P(A)+P(B) 

DISJOINT EVENTS

r

A+B=0

CLASSICAL APPROACH

r

P(A)=     #OF OUTCOMES OF A            TOTAL # OF OUTCOMES

PROBABILITY OF AT LEAST ONE

r

P(AT LEAST ONE WHATEVER) = 1 - P( 0 WHATEVERS)AT LEAST ONE MEANS ONE OR MORE AND THE COMPLEMENT  OF THIS IS NONE.

CONDITIONAL PROBABILITY

r

P(B GIVEN A) = P(A and B)                          P(A) KEYWORDS: GIVEN, IF

FACTORIAL RULE

r

n! = 1*2*3*4*5*6...n THIS RULE STATES THAT THE FACTORIAL OF N IS THE MULTIPLICATION OF ALL FACTORS BEFORE N AND INCLUDING N

COMBINATIONS RULE

r

nCr=    n!        (n-R)!*r! ORDER DOES NOT COUNT!!! 

RELATIVE FREQUENCY

r

P(A)= #OF TIMES A IS OBSERVED               TOTAL # OF TRIALS

COMPLEMENT OF EVENTS

r

P(A) + P(COMPLEMENT A) = 1 P(A) = 1 - P(COMPLEMENT A) P(COMPLEMENT A) = 1 - P(A) 

MULTIPLICATION RULE

r

KEYWORD: AND

INDEPENDENT

r

P(A and B) = P(A) * P(B)

DEPENDENT

r

P(A and B) = P(A)*P(B GIVEN A)

FUNDAMENTAL COUNTING RULE

r

THIS RULE STATES THAT  M*N IF THERE ARE M WAYS THAT AN EVENT CAN OCCUR AND THE SECOND EVENT CAN OCCUR N WAYS.

PERMUTATIONS

r

nPr =       n!          n1!*n2!*... WHERE n1+n2+n3 = n           ORDER COUNTS!!!!!