Conditional Probability Worksheet
P(A B) =
P( A and B)
P( B)
Exercises 1-4, compute the conditional probabilities P  A B  and P  B A 
1. P  A   0.7, P  B   0.4, P  A
B   0.25
2. P  A   0.45, P  B   0.8, P  A
B   0.3
3. P  A   0.61, P  B   0.18, P  A
4. P  A   0.2, P  B   0.5, P  A
B   0.07
B   0.2
Exercises 5-8, use the data in the table below, which shows the employment status of individuals
in a particular town by age group.
Age Group
0-17
18-25
26-34
35-49
50+
Total
Full-time
24
185
348
581
443
Part-time
164
203
67
179
162
Unemployed
371
148
27
104
173
Total
5. If a person in this town is selected at random, find the probability that the individual is employed
part-time, given that he or she is between the ages of 35 and 49.
6. If a person in the town is randomly selected, what is the probability that the individual is
unemployed, given that he or she is over 50 years old?
7. A person from the town is randomly selected; what is the probability that the individual is
between 0 and 17 given that they are employed full-time?
8. A person from the town is randomly selected; what is the probability that the individual is
between 26 and 34, given that they are unemployed?
Exercises 9-12, use the data in the following table, which shows the results of a survey of 2000
gamers about their favorite home video game systems, organized by age group. If a survey
participant is selected at random, determine the probability of each of the following.
0-12
13-18
19-24
25+
Total
Sony PS 2
63
105
248
191
607
Microsoft Xbox
84
139
217
166
606
Nintendo GameCube
55
92
83
88
318
Sega Dreamcast
51
113
169
136
469
Total
253
449
717
571
2000
9. The participant prefers the Sony PlayStation 2 system.
10. The participant prefers the Microsoft Xbox, given that the person is between the age of 13 and
18.
11. The participant prefers Nintendo GameCube, given that the person is between the ages of 19
and 24.
12. The participant is under 12 years of age, given that the person prefers the Sega Dreamcast
machine.
In Exercises 13-16, a snack-size bag of M&Ms candies is opened. Inside, there are 12 red
candies, 12 blue, 7 green, 13 brown, 3 orange, and 10 yellow. Three candies are pulled from the
bag in succession, without replacement.
13. Determine the probability that the first candy drawn is blue, the second is red, and the third is
green.
14. Determine the probability that the first candy drawn is brown, the second is orange, and the
third is yellow.
15. What is the probability that the first two candies drawn are green and the third is red?
16. What is the probability that the first candy drawn is orange, the second is blue, and the third is
orange?
In Exercises 17-20, three cards are dealt from a shuffled standard deck of playing cards.
17. Find the probability that the first card dealt is red, the second is black, and the third is red.
18. Find the probability that the first two cards dealt are clubs and the third is a spade.
19. What is the probability that the three cards dealt are, in order, an ace, a face card, and an 8?
(A face card is a jack, queen, or king.)
20. What is the probability that the three cards dealt are, in order, a red card, a club, and another
red card?
In Exercises 21-24, determine whether the events are independent.
21. A single die is rolled and then rolled a second time. .
22. Numbered balls are pulled from a bin one-by-one to determine the winning lottery numbers.
23. Numbers are written on slips of paper in a hat; one person pulls out a slip of paper without
replacing it, then a second person pulls out a slip of paper.
24. In order to determine who goes first in a game, one person picks a number between 1 and 10
and doesn’t tell the other person, then a second person picks a number between 1 and 10.
25. A bag contains five red marbles, four green marbles, and eight blue marbles. Find the
probability of pulling two red marbles followed by a green marble if the marbles are pulled from the
bag
a. with replacement.
b. without replacement.
26. A box contains three medium t-shirts, five large t-shirts, and four extra-large t-shirts. If
someone randomly chooses three t-shirts from the box, find the probability that the first t-shirt is
large, the second is medium, and the third is large if the shirts are chosen
a. with replacement.
b. without replacement.
27. Draw a Venn Diagram and then answer the questions.
28. Draw a Venn Diagram and then answer the questions.
a. Find the probability that a teacher selected at random said that lack of parental support is the
only problem hampering a student’s schooling?
b. Find the probability that a teacher selected at random said that the lack of parental support OR
abuse hampers a students schooling?
c. What is the probability that teacher thinks that none of these problems hampers a student’s
schooling?
d. What is probability that a teacher thinks that only malnutrition hampers a student’s schooling?
29. Draw a Venn Diagram and then answer the questions.
30. A die is rolled. What is the probability that the number is even or less than 4?