4.2 Probability Rules

mutually exclusive events

two events are this if they share no common outcomes - these are sometimes called disjoint events

∪

a mathematical symbol representing the union of sets; also represents “or” - the notation P(A∪B) is read as “the probability of A or B”

addition rule

if A and B are mutually exclusive/disjoint events, then the probability of A or B is the sum of the probability of A and the probability of B - can be expressed with the notation P(A∪B) = P(A) + P(B)

independence (informally)

two events are this if learning that one event occurs does not change the probability that the other event occurs

complement

the this of an event is the subset of outcomes in the sample space that are not in the event

legitimate assignment of probabilities

an assignment of probabilities to outcomes is this if each probability is between 0 and 1 inclusive and the sum of the probabilities is 1

subjective probability

a probability that represents someone’s personal degree of belief

probability assignment rule

a rule that states that the probability of the entire sample space must be 1 - can be expressed using P(S) = 1

∩

a mathematical symbol that represents the intersection of sets; it also represents “and” - the notation P(A∩B) is read as “the probability of A and B”

multiplication rule

if A and B are independent events, then the probability of A and B is the product of the probability of A and the probability of B - can be expressed using the notation P(A∩B) = P(A) * P(B)

complement rule

a rule that states that the probability of an event occurring is 1 minus the probability that it doesn’t occur - can be expressed using P(A^C) = 1-P(A)

A^C

notation for the complement of event A

probability

a number between 0 and 1 that reports the long-run frequency that an event will occur - the notation P(A) is read as “the probability of event A”