Unit 11 Flashcards
Equation for: one item from a group of “m” items time a second item from a group of “n” items
mxn
permutation equation and rules
nPr=n!/(n-r)! & no item reused, are distinct, and order matters
non-distinct permutation equation
n!/p!q!r!
combination equations and rules
nCr=n!/(n-r)!r! & no item reused, are distinct, and order doesn’t matter
Equation for ‘find the probability of’
0≤prob≤1
P(E)=n(E)/n(S)
Equation for ‘find the probability of OR’
P(A)+P(B)-P(A&B)
Probability of an Event NOT occurring equations
P(S)=P(E)+P(NOT E)
P(NOT E)=1-P(E)
Odds in FAVOR of an Event
a:b which is ‘a to b’
P(E)/P(NOT E)
Odds AGAINST an Event
b:a which is ‘b to a’
P(NOT E)/P(E)
Formula for AND probability of TWO OR MORE ‘independent events’
P(E AND F)=P(E)xP(F)
Formula for AND probability of TWO OR MORE ‘dependent events’
P(E AND F)=P(E)xP(F given that E has occurred)
EX: You have 9 books to place on a bookshelf w/ only 4 spots. How many ways can you place them?
9!/(9-4)!=3,024
EX: 5-digit code with 3 letters & 2 digits. How many possible codes?
26x26x26x10x10=1,757,600
EX: How many diff arrangements possible for 10 flags if 3 are red, 5 blue, and 2 white?
10!/3!5!2!=2,520
EX: Committee of 4 people with 2 women and 2 men chosen from 6 women and 4 men. How many possible ways can you form committee?
6C2x4C2=15x6=90
EX: S=family w/ 3 kids
{BBB,BBG,BGB,BGG,GGG,GGB,GBG,GBB}
Find prob fam has:
a) P(girl first)
b) P(exactly 2 boys)
S=2x2x2=8
a) P(girl first)=4/8/1/2
b) P(exactly 2 boys)=3/8
EX: S=rolling 2 dice
Find prob of getting:
a) P(roll w/ even #s)
b) P(sum=7)
S=6x6=36
a) E={(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)}
P(roll w/ even #s)=9/36=1/4
b) E={(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)}
P(sum=7)=6/36=1/6
EX: You pick 5 cards from 52 deck. What is prob you pick exactly 3 clubs?
C(13,3)xC(39,2)/C(52,5)=0.0815
EX: City Council of 8 Dems and 8 Reps. If committee of 5 is selected, find prob of 2 Dems and 3 Reps?
C(8,2)xC(8,3)/C(16,5)=14/39
EX: Find prob of NOT rolling a dice #<5
P(NOT #<)=1-P(#<5)=6/6-4/6=2/6=1/3
EX: Find prob you pick a card and it is a 7 OR Club card
P(7)+P(Club)-P(7&Club)=4/52+13/52-1/52=16/52=4/13=0.307
EX: 1 card from 52. Find odds against drawing a Black Jack
P(Not BJ)/P(BJ)=(50/52)/(2/52) =50/52x52/2=25/1
25:1 which is 25 to 1
EX: What are the odds it will rain if the probability is 20%?
P(rain)/P(Not rain)=(1/5)/(4/5)=1/5x5/4=5/20 which is 1:4
EX: Find prob you roll a die and get a #<5 AND you flip a coin and get tails
P(#<5)xP(tails)= 4/6x1/2= 4/12= 1/3
EX: Find prob you pick 2 cards w/out replacement and you get a Club AND Diamond
P(Club)xP(Diamond given Club has occurred)= 13/52x13/51= 0.064
