Name:
Date:
CONDITIONAL PROBABILITY
Let A and B be events in a sample space. RECALL
 the probability of A and B is P( A  B )
 the probability of A or B is P( A  B )
VOCABULARY
Conditional Probability is the probability of an event given an event. For example, the probability of A given B is
written as P(A | B). Similarly, the probability of B given A written as P(B | A). Recall and
① Suppose that 70% of a
Home (H)
population is homeowners
(H), 85% are car owners (C),
and 60% own homes and
cars (H C).
No Home (~H)
Total
Car (C)
No Car (~C)
Total
A
B
C
D
E
F
G
H
I
J
K
L
What is the probability of a …
homeowner given a car owner?
car owner given a homeowner?
non-homeowner given a car owner?
car owner given a non-homeowner?
homeowner given a non-car owner?
Probability as Reduced Ratio
non-car owner given a homeowner?
non-homeowner given a non-car owner?
non-car owner given a non-homeowner?
car owner but not a homeowner?
homeowner but not a car owner?
non-homeowner and non-car owner?
car owner or homeowner?
② In a town of drivers, 20%
are youths (Y), 40% are
grown-ups (G) and the rest
are elders (E). 16% cause
accidents (A) – 2% from
youths, 8% from elders and
the rest from grown-ups.
A
B
C
D
E
F
G
H
I
J
K
L
Notation
Youths (Y)
Grown-Ups (G)
Elders (E)
Total
Accidents (A)
No Accidents (~A)
Total
What is the probability of …
an accident given the driver is a youth?
an accident given the driver is a grown-up?
an accident given the driver is an elder?
no accident given the driver is a youth?
no accident given the driver is a grown-up?
no accident given the driver is an elder?
the driver is a youth given an accident?
the driver is a grown-up given an accident?
the driver is an elder given an accident?
the driver is a youth given no accident?
the driver is a grown-up given no accident?
the driver is an elder given no accident?
Notation
Probability as Reduced Ratio
Name:
Date:
CONDITIONAL PROBABILITY
③
For #3-5, make a chart and write the notation and reduced ratio for each probability.
In a math class, 30% are
math majors (M), 50% are
engineers (E) and the rest
are other majors (O). 49%
of the class is passing
including 18% for math and
25% for engineering.
A
B
C
D
E
F
G
H
I
J
K
L
What is the probability of …
a math major given a passing student?
an enginnering major given a passing student?
another major given a passing student?
Notation
Probability as Reduced Ratio
a math major given a failing student?
an enginnering major given a failing student?
another major given a failing student?
a passing student given a math major?
a passing student given an engineering major?
a passing student given another major?
a failing student given a math major?
a failing student given an engineering major?
a failing student given another major?
④ The probability that it will
snow on February 5 (F5) is
30%. The probability that it
will snow on February 6
(F6) is 47%. The
probability that it snows on
both days is 12%.
A
B
C
D
E
F*
What is the probability of …
snowing on Feb 5 given it snows on Feb 6?
not snowing on Feb 5 given it snows on Feb 6?
snowing on Feb 6 given it snows on Feb 5?
not snowing on Feb 6 given it snows on Feb 5?
snowing on the two days?
snowing on one day but not the other?
Notation
Probability as Reduced Ratio
⑤ In a stadium of three sections, 50%
of fans are in section 1 (S1), 30% in
section 2 (S2) and the rest in section
3 (S3). The attendance rate is 47%
with 20% in Section 1, 15% in
Section 2 and the rest in Section 3.
A
B
What is the probability of a fan …
from Section 2 given the fan does not attend?
does not attend given the fan is from Section 2?
Notation
Probability as Reduced Ratio