
AND=
OR=
 Multiply, independent events?
 Add, mutually exclusive?

Fundamental Counting Rule
In a sequence of events (like choosing what piece of clothes to wear), multiply the numbers together to get the total number of combinations possible.

Permutations
Key words
 When order matters!
 "arrange, order, rearrange, rank, sequence, in how many ways can things be ordered"

Permutation formulas
number of permutations of n objects: n! (arrange)
 nPr= n!÷(nr)! (selected piece and arrange them)
 n= # of objects (bigger #)
 r= selected # (smaller #)

Combinations
Key Words
 Order doesn't matter!
 "choose, select, team, committee"

Combinations formula
 nCr= n!÷(nr)!r!
 n= # of objects (bigger #)
 r= selected # (smaller #)

Pascals's triangle
 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1

Probability of 0
Probability of 1
 0= event never occurs
 1= event always occurs

Drawing a sample space
tossing a coin
tossing 2 coins
rolling a die
 heads tails
 HH TT HT TH
 1 2 3 4 5 6

Classical probability formula
Prob.= (# of successful outcomes)÷(# of total outcomes)

The Compliment
 opposite of event
 1fraction probability= compliment

Mutually Exclusive
2 events that can't occur at the same time, only use the word OR with this condition

When things are not mutually exclusive
add two conditions and subtract overlap
 Example:
 P(king) + P(club)  P(king of clubs)
 4/52 + 13/52  1/52

Independent Events
if event A doesn't affects the probability of event B
P(A AND B)= P(A) • P(B)

When events are not independent
Don't forget to reduce the denominator by one for each next fraction because you wouldn't be returning "the marbles to the bag"

When doing a tough word problem
REWRITE THE QUESTION. Find out what you need and write out what you're finding the probability for.
Example: P(1st yes AND 2nd yes AND 3rd yes)

Conditional Probability
conditional statement using the words "if" or "given that"

Conditional Probability formula
P(B given A)= P(A and B) ÷ P(A)

