# Probability

## Terms

undefined, object
copy deck
Define 'Random'
Random if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions
Define 'Probability'
The proportion of times an outcome would occur in a very long series of repetitions.
Define 'Sample space "S"'
The set of all possible outcomes.
ex: S={1,2,3,4,5,6,7}
Deinfe 'probability model'
For a random phenomenon, consists of a sample space 'S' and an assignment of probabilities 'P'.
Define 'Compliment'
For event A, the compliment consists of exactly the outcome NOT in A.

ex: if P(A)=80%, then P(A Compliment)=20%
Define 'Disjoint'
Events A and B are disjoint if they have NO outcomes in common.

(**Do NOT confuse this with independence! Events _can_ be both disjoint and dependent, even though it rarely happens**)
Define 'Independent'
Knowing that one event occurs does not change the probability we would assign to the other event.
P(A or B) = P(A) + P(B)
Multiplication rule for independent events
P(A and B) = P(A) x P(B)
Compliment rule
P(A Compliment) = 1 - P(A)
Define 'Union'
For events A and B, contains all of the outcomes in both A and B.
Define 'intersection'
The events that ALL of the events occur together.

ex: Out of 100 people, 80 people took STATS, 30 people took Psychology, and thus 10 people took STATS and Psychology (this is an intersection).
How do you know if events are independent?
In terms of conditional probability, events are ndependent if P(A/B) = P(B)
Conditional Probability
This si the probability of one event under the condition that we know another event.

Ex: Give the % of students who are enrolled in AP Statistics given that they are female.

The multiplication rule for the union of two events in terms of conditional probability is:

P (B/A)= P(A) x P(B/A), where B"/"A means B "given" A.

The definition of conditional probability when P(A) > 0 is:

P(A/B)= P(A and B)
----------
P(A)

14