
Independent
if the occurrence, or nonoccurrence of one event in
no way affects the probability of another.

Conditional (dependent) –
if the probability of one Event depends on
another Event having taken place before.
Addition Law The Probability of 2 events
P(A
B) where
is the union meaning the probability that either A or B
occurs, or both.
P(A
B) = P(A or B)
P(A or B) = P(A) + P(B) – P(A and B)
P(A
B) = the intersection of A and B.
Mutually Exclusive Events
If A and B are
Mutually Exclusive Events,
then P(
A
B) = 0.

They have no sample points in common, which means that when one
occurs the other one cannot occur.

In this case the addition law becomes: P(
A
B) = P(A) + P(B)
Conditional Probability
P
(
B

A
)
=
P
(
A B
)
P
(
A
)
=
P
(
A
∧
B
)
P
(
A
)
P(BA) = conditional probability (The Probability of B given A)
The General Multiplication Rule
This is used to estimate the intersection
P(
A
B) of two events, or
otherwise the probability of P(A and B). It is based on the definition of
conditional probability.
P
(
B

A
)
=
P
(
A B
)
P
(
A
)
If the probability of A depends
on the probability of B occurring first, then P(A and
B) = P(AB) x P(B) and P(A and B) = P(BA) x P(A)
If A and B are independent
events, then the probability of A and
B occurring is
the product of the 2 probabilities.
P (A and B) = P(A) x P(B)
Checking for Independence
P(A
B) = P (A) x P(B) then events are
independent
P(A
B)
≠
P(A) x P(B) then events are
not independent
Tree Diagram

A tree diagram is a graphical representation of probabilities

Each outcome is represented by a branch
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 Summer '20
 Conditional Probability, Probability, Probability theory, Probability space, outcome E P