Transcript A.P. STATISTICS LESSON 6.3 (DAY 1)

AP STATISTICS
LESSON 6.3
(DAY 1)
GENERAL PROBABILITY RULES
Warm – up # 1
Page 323 # 5.87
ESSENTIAL QUESTION:
What are general probability rules
and how are they used to solve
probability problems?
Objectives:
 To become familiar with general probability
rules.
 To use the general probability rules to solve
problems.
 To use Venn diagrams, Tree diagrams and
tables to solve probability problems.
Rules of probability
Rule 1: 0 ≤ P(A) ≤ 1 for any A.
Rule 2: P(S) = 1
Rule 3: Compliment rule: For any event A,
P(Ac) = 1 – P(A)
Rule 4: Addition rule: If A and B are
disjoint events, then
P(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)
Union
The union of any collection of events is the
event that at least one of the collection
occurs.
S
B
A
C
The addition rule for disjoint events: P(A or B or
C ) = P(A) + P( B) + P(C) when events A, B,
and C are disjoint.
Addition rule 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)
This rule extends to any number of disjoint
events.
Example 6.16
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The general addition rule for the union
of two events:
P(A or B) = P(A) + P(B) – P(A and B)
A and B
B
A
P ( A and B ) is called joint probability.
General addition rule for 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 U B ) = P(A) + P(B) – P( A ∩ B )
Example 6.17
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Conditional Probability
P(A/B) – Conditional probability – gives the
probability of one event under the
condition that we know another event.
Example 6.19
 Page 366
General Multiplication Rule for any
Two Events
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.
In words, this rule says that for both of two events
to occur, first one must occur and then, given
that the first event has occurred, the second
must occur.
Example 6.20
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Definition of conditional probability
When P(A) > 0, the conditional probability of
B given A is
P(A/B) = P( A and B)
P (A)
Be sure to keep in mind the distinct roles in
P(B/A) of the event B whose probability we
are computing and the event A that
represents the information we are given.
Example 6.21
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