Secondary II – Unit 1 Probability – Conditional Probability Name_____________
P(A B) =
P( A and B)
P( B)
Exercises 3-6, compute the conditional probabilities P  A B  and P  B A 
𝑃(𝐴|𝐵) = .0625 𝑃(𝐵|𝐴) = .357
𝑃(𝐴|𝐵) = .375 𝑃(𝐵|𝐴) = .6
𝑃(𝐴|𝐵) = .39 𝑃(𝐵|𝐴) = .113
𝑃(𝐴|𝐵) = .4 𝑃(𝐵|𝐴) = 1
Exercises 7-10, 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+
Full-time
24
185
348
581
443
Part-time
164
203
67
179
162
Unemployed
371
148
27
104
173
7. 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.
.207
8. 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?
.222
9. A person from the town is randomly selected; what is the probability that the individual is employed
full-time, given that he or she is between 18 and 49 years of age?
.605
10. A person from the town is randomly selected; what is the probability that the individual is
employed part-time, given that he or she is at least 35 years old?
.208
Exercises 11-14, 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+
Sony PlayStation 2
63
105
248
191
607
Microsoft Xbox
84
139
217
166
606
Nintendo GameCube
55
92
83
88
318
Sega Dreamcast
51
253
113
449
169
717
136
571
469
2000
11. The participant prefers the Sony PlayStation 2 system.
.3035
12. The participant prefers the Microsoft Xbox, given that the person is between the age of 13 and 18.
.31
13. The participant prefers Nintendo GameCube, given that the person is between the ages of 13 and
24.
.15
14. The participant is under 12 years of age, given that the person prefers the Sega Dreamcast
machine.
.11
15. A pair of dice are tossed. Find the probability that the sum on the two dice is 8, given that the sum
is even.
5/18
16. A pair of dice are tossed. Find the probability that the sum on the two dice is 12, given that
doubles are rolled.
1/6
17. A pair of dice are tossed. What is the probability that doubles are rolled, given that the sum on the
two dice is less than 7?
1/5
18. A pair of dice are tossed. What is the probability that the sum on the two dice is 8, given that the
sum is more than 6?
5/21
19. What is the probability of drawing two cards in succession (without replacement) from a standard
deck and having them both be face cards?
.05
20. Two cards are drawn from a standard deck without re- placement. Find the probability that both
cards are hearts.
.06
21. Two cards are drawn from a standard deck without replacement. What is the probability that the
first card is a spade and the second card is red?
.13
22. Two cards are drawn from a standard deck without replacement. What is the probability that the
first card is a king and the second card is not?
.07