Flashcards stats 2C-2D

probability model

a description of a random process that consists of two parts: a list of all possible outcomes and the probability of each outcome.

A valid probability model must obey two common-sense rules:

The probability of any event is a number between 0 and 1, inclusive.

o All possible outcomes in the sample space must have probabilities that add up to 1.

The list of all possible outcomes is called the______

sample space

event

a subset of the possible outcomes from the

sample space of a random process.

an event is usually denoted by_____

capital letters

A probability model does more than just assign a probability to each outcome— it allows us to_____

find the probability of an event.

The complement rule equation

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

A^c

Complement of A (event A does not happen)

Two events A and B are mutually exclusive if____

exclusive if they have no outcomes in common and so can never occur together

Two events A and B are mutually exclusive if P(A and B) =______

0

The addition rule for mutually exclusive events

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

Venn Diagram

consists of one or more circles surrounded by a rectangle.

The region inside the rectangle of a venn diagram represents the

sample space of the random process

each circle in a venn diagram represents an

event

If p and s are any two events resulting from the same random process, the general addition rule says that—

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

The event "A and B" is called the ________________________________________ of events A and B.

intersection

all outcomes in the sample space of events A and B that are common to both events, and is denoted

A∩B

The event "A or B" is called the ______________________________ of events A and B.

union

all outcomes in the sample space that are in event p, event s, or both, and is denoted

A∪B

complement of A

A ∩ B

A or B

P(A∪ B) =

P(A) + P(B) − P(A ∩ B)

The probability that one event happens given that another event is known to have happened is called a____

conditional probability.

probability. The conditional probability that event p happens given that event s has happened is denoted by________

P(A | B)

Is there a connection between conditional probability and conditional relative frequency?

yes

A conditional probability is just a conditional relative frequency that comes from a______

a random process

P(A|B) =

P(A and B)/P(B)

Events p and s are independent if knowing whether or not one event has happened______

does not change the probability that the other event will happen.

P(A|B) =

P(AIB^c) = P(A)

If events p and s are NOT independent, then the occurrence of one event ______change the probability that the other

event will happen,

will

Multiplication Rule

To determine the probability, we multiply the probability of one event by the probability of another given the first one

multiplication rule equation

P(A and B) = P(A) x P(B I A)

P(AIB = P(A ∩ B)/P(B) → P(A ∩ B) =

P(B) x P(A I B)

A tree diagram shows the sample space of______

a random process involving multiple stages.

tree. All probabilities after the first stage are______

conditional probabilities

The multiplication rule for independent events says that if p and s are independent events, the probability that p

and s both occur is—

P(A ∩ B) = P(A) ∙ P(B)

The multiplication rule for independent events is just a special case of the general multiplication rule, in

which P(A | B) =

P(A)

The multiplication rule for independent events q(p ∩ s) = q(p) ∙ q(s) gives us another way to determine whether

two events are

independent.

Is there a connection between mutually exclusive and independent?

Yes

Two mutually exclusive events with non-zero probabilities can _____be independent,

never

for two mutually exclusive events with non-zero probabilities, if one event happens, the other event is ________ not to happen.

guaranteed

General addition rule:

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

Mutually Exclusive Events

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

General Multiplication Rule

P(A and B) = P(A) * P(B|A)

Independent Events

P(A and B) = P(A) ∙ P(B)