stats exam 2 vocab and equations

complement

an event A consists of all outcomes in the sample space that are NOT in A

• denoted by A^C

• probability that the event A does NOT occur

• “randomly selected”

complement rule

P(A^c) = 1 - P(A)

mutually exclusive events - unions and intersections

two events A or B are mutually exclusive (or disjoint) if they FO NOT have any common outcomes

• can’t happen at the same time

• don’t overlap

• “fair”

intersection

two events A and B consists of the outcomes in both A AND B

• “ ^ “

• gets listed once

union

two events A and B consists of the outcomes that are in A OR B

• “ v “

• whats in both (venn diagram)

addition rule - probability of the union of two events

P(A v B) = P(A) + P(B) - P(A ^ B)

addition rule - mutually exclusive

(A v B) = P(A) +P(B)

independent

two events are independent if knowing whether one event occurs does not affect the probability that the other event occurs

• when two events are independent, the probability of their intersection is easy to compute

• can be extended for three or more independent events

multiplication rule - probability of the intersection of independent events

P(A ^ B) = P(A) * P(B)

• “independently”

multiplication rule - computing losses

P(at least one) = 1 - P(none)

• easier to find at least one probabilities using the complement rule