Probability Rules

"or" probability

probability A or B or both occur

"and" probability P(A and B)

probability both events occur

conditional probability P(B|A)

probability of B, given A has occurred

marginal probability P(A)

probability of a single event (characteristic)

events

subset of s

You can show that P(B|A) = P(A and B)/P(A)

true

if A and B are independent then P(A or B) becomes P(A) + P(B) - P(A)P(B)

true

independent events

two events (or characteristics) A and B have outcomes that do not affect each other - P(A|B) = P(A) - P(B|A) = P(B) - P(A|B) = P(A|Not B) - P(A and B) = P(A) * P(B)

complement

- complement of a is the set of all outcomes in s which are not included in A - everyone who does not have characteristic A - probability of what you do want = 1 - probability of what you do not want

disjoint events

- events that cannot occur at the same time - P(A and B) = 0 - P(A or B) = P(A) + P(B)

conditions to be independent

- random sample - experiment - in problem

P(A and B)

P(A) * P(B|A)

P(A or B) : "A or B or both", "at least one"

P(A) + P(B) - P(A and B)

complement rule

P(Ac) = 1 - P(A)

suppose the probability of someone being female and voting for candidate A is 30%. what is the notation?

P(female and voting for A) = 0.30

suppose 90% of the patients who test positive for a disease actually have the disease. write this as a probability

P(have disease | test positive) = 0.90

probability of an event P(A)

long term chance of A occuring

suppose you make 10 telemarketer calls. which of the following is the complement of "at most" 9 sales?

more than 9; all 10

sample space (s)

all possible outcomes

when is P(A or B) = P(A) + P(B)

disjoint events