Probability Rules

P(E or F) = P(E) + P(F) - P(E and F)

Prob of E or F happening

P(E and F) = P(E) × P(F)

Prob of two events happening

Prob of one event and then another

(Independant Events)

With Replacement

P(E and F) = P(E) × P(F\E)

Prob of one event and then another

(Dependant Events)

Without Replacement

P(E^c) = 1−P(E)

Used when the prob of E is Difficult to find 

Also when doing at least 

P(E\F) = P(E and F) / P(E)

Prob of F given that E has occured

p × q × r … 

How many different ways a sequence of events can happen

nPr = n! / (n-r)!

How many different ways a subset r,

can be taken from n distinct items

where the order matters (no repetitions)

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

How many different ways a suubset r,

can be taken from n distinct irems where

the order does’t matter (no repetitions)

n! / (n₁! n₂! ... n_k!)

Number of ways a set, n, that has 

subsets non-distinct items can be arranged