More Problems from Conditional Probability
I. Wake Forest University recorded the statistics shown below in the table for its
1992 – 1993 annual giving campaign:
Contributed
Did not contribute
1970
192
174
Class
1980
182
260
1990
325
586
If a person is randomly selected from the population described in the table above, find
the probability that the person
(1) did not contribute, given that this person is in the class of 1980.
(2) contributed, given that this person is in the class of 1990 or 1970.
(3) is in the class of 1970, given that this person contributed.
(4) is in the class of 1990, given that this person did not contribute.
(5) is not in the class of 1980, given that this person contributed.
II. The table shows accident data for 346 accidents:
Fatal
Non-Fatal
Small
67
128
Size of Car
Medium
26
63
Large
16
46
If an accident is randomly selected from the accidents described in the table
above, find the probability that the accident
(1) involved a small car, given that there was a fatality in the accident.
(2) did not involve a small car, given that was no fatality in the accident.
(3) involved a fatality, given that a small car was involved.
(4) did not involve a fatality, given that a small car was not involved.
(5) involved a fatality, given that large car was not involved.
III. A survey of 75 college students was taken to determine where they got the news
about what’s going on in the world. Of those surveyed, 29 students got the news
from newspapers, 43 from television, and 7 from both newspapers and television.
If a student is randomly selected from those who were surveyed, what is the
probability that the student
(1) got the news from the television or the newspapers?
(2) got the news from newspapers, given that the student also got the news from
television?
(3) got the news from television, given that the student also got the news from
newspapers?
IV. An anonymous survey of college students was taken to determine behaviors
regarding alcohol, cigarettes, and illegal drugs. The results were as follows:
894 drank alcohol regularly, 665 smoked cigarettes, 192 used illegal drugs,
424 drank alcohol regularly and smoked cigarettes, 114 drank alcohol regularly
and used illegal drugs, 119 smoked cigarettes and used illegal drugs, 97 engaged
in all three behaviors, and 309 engaged in none of these behaviors.
(1) How many students were surveyed?
If a random student from this survey is taken, what is the probability that this student
(2) used illegal drugs?
(3) used illegal drugs, given that the student drank alcohol regularly?
(4) drank alcohol regularly, given that the student used illegal drugs?
(5) drank alcohol regularly and smoked cigarettes, but did not use illegal drugs?
(6) drank alcohol regularly and smoked cigarettes, given that the student did not use
illegal drugs?
(7) drank alcohol regularly or used illegal drugs, but did not smoke cigarettes?
(8) drank alcohol regularly or used illegal drugs, given that the student did not
smoke cigarettes?
(9) engaged in exactly two of these behaviors?
Solution Key
I. (1) 58.8%
(2) 40.5% (3) 27.5% (4) 57.5% (5) 74.0%
II. (1) 61.5% (2) 46.0% (3) 34.4% (4) 72.2% (5) 32.7%
III. (1) 86.7%
(2) 16.3% (3) 24.1%
IV. (1) 1500
(6) 25%
(2) 12.8% (3) 12.8% (4) 59.4% (5) 21.8%
(7) 35.1% (8) 63.0% (9) 24.4%