AP Statistics Unit 4- Probability

law of large numbers

relative frequency tends to get closer and closer to a certain number (the probability) as an experiment is repeated more times

independent events

Outcome of one event does not change the outcome of subsequent trials

P(A)

probability of event A happening

A^c

complement of event A (outcomes NOT in event A)

mutually exclusive (disjoint)

events that have no event in common, CANNOT be independent and occur at the same time

union

the event of A or B happening (denoted by U)

intersection

the event of A and B happening (denoted by ∩)

probability

denoted by P(event), P(E)= favorable outcomes/total outcomes

legitimate values

for any event e, 0 less than or equal to P(E) less than or equal to 1

sample space

if S is the sample space, P(S)=1

complement

for any event E, P(E)+P(not E)=1

multiplication rule→ if independent

P(A&B)= P(A) x P(B)

multiplication general rule

P(A&B)= P(A) x P(B|A)

addition rule→ if disjoint (mutually exclusive, so NOT independent)

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

addition general rule (if E&F are not disjoint)

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

at least 1

the probability that at least 1 outcome happens is 1-the probability that no outcomes happen P(at least 1) = 1-p(none)

conditional probability

a probability that takes into account a given condition: P(B|A)= P(B and A) / P(A) , P(and)/P(given)

mutually exclusive check

if p(A and B)= 0, then mutually exclusive, if P(A and B)= P(A) x P(B), then independent

independence check

if P (A and B)= P(A) x P(B) then A and B are independent events.