Stats Ch. 6

addition rule (unions of two events)

For any two events A and B, P(A or B) = P(A) + P(B) - P(A and B) Equivalently,P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

addition rule (disjoint)

P(one or more of A, B, C) = P(A) + P(B) + P(C)

multiplication rule (independent events) rule 5

Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. If A and B are independent, P(A and B) = P(A)P(B) This is the multiplication rule for independent events.

{A ∪ B}

{A or B}

probability

long-term relative frequency or the proportion of times the outcome would occur in a very long series of repetitions

with replacement

replacing the object after drawn to create an equal draw for the next round

chance behavior is unpredictable in the _______ run but has a regular and predictable pattern in the ______ run

short, long

tree diagrams and the multiplication rule

the probability of reaching the end of any complete branch is the product of the probabilities written on its segments

sample space S

the set of all possible outcomes in a random phenomenon

The probability that an event does not occur is 1 minus the probability that the event ______.

does occur

random

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

Multiplication Principal

If you can do one task in a number of ways and a second task in b number of ways, then both tasks can be done in a x b number of ways

probability rule three

The complement of any event A is the event that A does not occur, written as Ac. The complement rule states that P(Ac) = 1 - P(A)

probability rule four

Two events A and B are disjoint (also called mutually exclusive) if they have no outcomes in common and so can never occur simultaneously. If A and B are disjoint, P(A or B) = P(A) + P(B) This is the addition rule for disjoint events.

probability model

a mathematical description of a random phenomenon consisting of two parts: a sample space S and a way of assigning probabilities to events

probability rule two

If S is the sample space in a probability model, then P(S) = 1.

conditional probability

When P(A) > 0, the conditional probability of B given A is P(B|A) = P(AandB) P(A)

Any probability is a number between ______

0 and 1

All possible outcomes together must have probability __________

1

conditional probability

P(A | B) it gives the probability of one event under the condition that we know another event

independent events

P(B | A) = P(B)

probability rule one

The probability P(A) of any event A satisfies 0 ≤ P(A) ≤ 1.

event

any outcome or a set of outcomes of a random phenomenon

Rules of Probability

Rule1. 0≤P(A)≤1for any event A. Rule 2. P(S) = 1. Rule 3. Complement rule: For any event A,P(Ac) = 1 - P(A) Rule 4. Addition rule: If A and B are disjoint events, thenP(A or B) = P(A) + P(B) Rule 5. Multiplication rule: If A and B are independent events, then P(A and B) = P(A)P(B)

general multiplication rule

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

If two events have no outcomes in common, the probability that one or the other occurs is the sum of their __________________.

individual probabilities

without replacement

not replacing the object after drawn, creates a new probability for the next event

independent

the outcome of one trial must not influence the outcome of any other