AP Statistics Ch. 6

independent

the outcome of one trial must not influence the outcome of any other; A and B are independent when P(B | A) = P(B); the multiplication rule for intersections then becomes P (A and B)= P(A) P(B)

addition rule

the probability of disjoint events is the sum of their individual probabilities. P (A or B) = P(A) + P(B)

conditional probability

the probability of one event under the condition that we know another event; when P(A) > 0, the conditional probability of B given A is: P(B | A) = P(A and B) / P (A)

joint probabality

the probability of the simultaneous occurrence of two events; P(A and B)

union

(A or B) contains all outcomes in A, in B, or in both A and B

joint event

the simultaneous occurrence of two events

intersection

(A and B); contains all outcomes that are in both A and B, but not outcomes in A alone or B alone

legitimate values

0 ≤ P(A) ≤ 1 for any event A

probability rules

1. All probability is a number between 0 and 1. 0≤ P(A) ≤ 1 2. All outcomes together must equal 1. P(S)=1 3. The probability that an event does not occur is 1 minus the probability that the event does occur. This is called the complement of the event. P(A complement) = 1- P(A) 4. If two events have no outcomes in common (disjoint) the probability that one or the other occurs is the sum of their individual probabilities. This is called the addition rule. P(A or B)= P(A) + P(B) 5. If the outcome of one event does not influence the next event (independent), multiply the probabilities of both events. This is called the multiplication rule. P(A and B)= P(A)·P(B)

general multiplication rule

the joint probability that both of two events A and B happen together can be found by P (A and B) = P (A) P(B | A). P (B | A) is the conditional probability that B occurs given the information that A occurs

equally likely outcomes

If a random phenomenon has k possible outcomes, all equally likely, then each individual outcomes has probability 1/k. P(A)=count of outcomes in A ÷ count of outcomes in S = count of outcomes in A ÷ k

multiplication rule

If the outcome of one event does not influence the next event, multiply the probabilities of both events. P(A and B)= P(A)·P(B)

total probability 1

P(S) = 1

event

an outcome or set of outcomes of a random phenomenon

probability model

consists of a sample space S and an assignment of probabilities P

general addition rule for the union of two sets

for any two events of A and B: P (A or B) = P(A) + P(B)− P(A and B)

addition rules for disjoint events

if events A,B, and C are disjoint in the sense that no two have any outcomes in common then: P(one or more of A,B,C)= P(A)+ P(B) + P(C)

multiplication principle

if you can do a task in A number of ways and a second task in B number of ways, then both tasks can be done in A × B number of ways

random

individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions

sample space S

is the set of all possible outcomes of a random phenomenon

complement rule

the complement of event A is exactly the outcomes that are not in A. P(complement of A)= 1− P(A)

law of large numbers

the idea that probability is based on observation and describes what happens in very many trials

probability

the proportion of times the outcome would occur in a very long series of repetitions -is "empirical". Can only be estimated from real world trials. -Probability is a number between 0 and 1. 0≤ P(A) ≤1 -The probability of any event is the sum of the probabilities of the outcomes making up the event. P(S)=1

disjoint

two events have no outcomes in common