Download AP Statistics Section 6.2 B Probability Rules

AP Statistics Section 6.2 B
Probability Rules
If A represents some event, then
the probability of event A
happening can be represented as
P(A)
_____
Probability
Rules
1. A probability must be a number
between 0 and 1 inclusive. Thus,
0  P(A)  1
for any event A, ____________
2. The sum of the probabilities of
all possible outcomes of some
“procedure” must equal ___.
1 If S is
the sample space in a probability
model, then P(S) = ____.
1
3. Two events are disjoint (also called
mutually exclusive) if they have no
outcomes in common (i.e. the events can
never occur simultaneously).
For example, rolling a pair of dice and
getting a sum of seven and rolling a pair of
dice and getting doubles would be
mutually exclusive events.
If A and B are disjoint, then
P(A or B) = P(A)
__________.
 P(B)
This is the addition rule for disjoint
events.
In place of “or” we may also use the

symbol for a “union” _____.
Similarly, we may use the
intersection symbol ______
 instead
 for the “empty
of “and” and ___
event” (i.e.
the event with no outcomes in it)
_________________________
If two events A and B are disjoint
we can write ___________
AB 
The probability that an event does not
occur is
1-probability the event does occur.
For an event A, the event that A
does not occur is called the
c
complement of A, written _____
A
The complement rule states that:
c
P(A )  1  P( A)
_______________.
Disjoint and complement are important terms
for us to understand. Perhaps we can use Venn
diagrams to clarify. In each case the large
rectangle represents our sample space.
Disjoint and complement are important terms
for us to understand. Perhaps we can use Venn
diagrams to clarify. In each case the large
rectangle represents our sample space.
A
A
c
Example: Consider the probabilities at the right
for the number of games it will take to complete
the World Series(WS) in any given year.
Note that each probability is between
0 and 1, and that the sum of the
probabilities is 1 because these 4
outcomes make up the sample space.
Example: Consider the probabilities at the right
for the number of games it will take to complete
the World Series(WS) in any given year.
Find: P(WS lasts 5 games)
.2121
Example: Consider the probabilities at the right
for the number of games it will take to complete
the World Series(WS) in any given year.
Find: P(WS does not last 5 games)
1  .2121  .7879
Example: Consider the probabilities at the right
for the number of games it will take to complete
the World Series(WS) in any given year.
Find: P(WS lasts 6 or 7 games)
.2323  .3737  .6060
Example: Consider the probabilities at the right
for the number of games it will take to complete
the World Series(WS) in any given year.
Find: P(WS lasts 8 games)
0
In the special situation where all
outcomes are equally likely, we
have a simple rule for assigning
probabilities to events.
If a random phenomenon has k
possible outcomes that are all equally
likely, then the probability of each
1
individual outcome is _____.
k
The probability of an event A is
number of outcomes in A
P(A) =
k