Section 8-3 Conditional Probability, Intersection, and Independence
Example 1. A company has rated 75% of its employees as satisfactory and 25% as unsatisfactory. Personnel
records indicate that 80% of the satisfactory workers had previous work experience while only 40% of the
unsatisfactory workers had any previous experience.
a. If a person with previous work experience is hired, what is the probability that this person will be a
satisfactory worker?
PSat  Exp
0.60
0.60
P( Sat | Exp) 


 0.857
P( Exp)
0.60  0.10 0.70
Satisfactory
Rating
Previous
Experience
Yes (0.8)
Prob
0.60
No (0.2)
0.15
Yes (0.4)
0.10
No (0.6)
0.15
Yes (0.75)
No (0.25)
b. If a person with no previous work experience is hired, what is the probability that this person will be a
satisfactory employee?
P( Sat  Exp' )
0.15
0.15
P( Sat | Exp' ) 


 0.5
P( Exp' )
0.15  0.15 0.30
Satisfactory
Rating
Previous
Experience
Yes (0.8)
Prob
0.60
No (0.2)
0.15
Yes (0.4)
0.10
No (0.6)
0.15
Yes (0.75)
No (0.25)
Example 2. A computer store sells three types of microcomputers; brand A, brand B, and brand C. Of the
computers they sell, 60% are brand A, 25% are brand B, and 15% are brand C. They have found that 20% of the
brand A computer, 15% of the brand B computers, and 5% of the brand C computers are returned for service
during the warranty period.
Brand
Defective Prob
Yes (0.20) 0.1200
A (0.60)
No (0.80) 0.4800
Yes (0.15) 0.0375
B (0.25)
No (0.85) 0.2125
Yes (0.05 0.0075
C (0.15)
No (0.95) 0.1425
a. If a computer is returned for service during the warranty period, what is the probability that it is a brand A
computer?
b. If a computer is returned for service during the warranty period, what is the probability that it is a brand B
computer?
c. If a computer is returned for service during the warranty period, what is the probability that it is a brand C
computer?
Example 3. In a random sample of 200 women who suspect that they are pregnant, 100 turn out to be pregnant.
A new pregnancy test given to these women indicated pregnancy in 92 of the 100 pregnant women and in 12 of
the 100 women who were not pregnant.
a. If a woman suspects she is pregnant and this test indicates that she is pregnant, what is the probability that she
really is
Pregnant
Test Result
Prob
pregnant?
Positive (0.92) 0.46
Yes (0.5)
P( preg  pos )
0.46
0.46
P( preg | pos) 


 0.885
P( pos)
0.46  0.06 0.52
Negative (0.08) 0.04
Positive (0.12) 0.06
No (0.5)
Negative (0.88) 0.44
b. If the test indicates that she is not pregnant, what is the probability that she really is pregnant?
P( preg | neg ) 
P( preg  neg )
0.04
0.04


 0.083
P(neg )
0.04  0.44 0.48
Pregnant
Test Result Prob
Positive (0.92) 0.46
Yes (0.5)
Negative (0.08) 0.04
Positive (0.12) 0.06
No (0.5)
Negative (0.88) 0.44
Example 4. In a given county, records show that of the registered voters, 45% are Democrats, 35% are
Republicans, and 20% are independents. In an election, 70% of the Democrats, 40% of the Republicans, and
80% of the independents voted in favor of a parks and recreation bond proposal.
Party
Vote
Prob
Yes (0.7) 0.315
Dem (0.45)
No (0.3) 0.135
Yes (0.4) 0.140
Rep (0.35)
No (0.6) 0.210
Yes (0.8) 0.160
Ind (0.20)
No (0.2) 0.040
a. If a registered voter chosen at random is found to have voted in favor of the bond, what is the probability that
the voter is a Republican?
b. If a registered voter chosen at random is found to have voted in favor of the bond, what is the probability that
the voter is an independent?
c. If a registered voter chosen at random is found to have voted in favor of the bond, what is the probability that
the voter is a Democrat?