Conditional Probability Worksheet

Conditional Probability Worksheet #3
𝑃(𝐴|𝐵) =
P( A  B)
or
P( B)
𝑃(𝐴 𝑎𝑛𝑑 𝐵)
𝑃(𝐵)
or
Name _______________________
𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝐴 𝑎𝑛𝑑 𝐵
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝐵
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+
Totals:
Full-time
24
185
348
581
443
Part-time
164
203
67
179
162
Unemployed
371
148
27
104
173
Totals:
7. If a person in this town is selected at random, find the probability that the individual is employed parttime, given that he or she is between the ages of 35 and 49.
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?
9. A person from the town is randomly selected; what is the probability that the individual is employed fulltime, given that he or she is between 18 and 49 years of age?
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?
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+
Totals
Sony PlayStation 2
63
105
248
191
607
Microsoft Xbox
84
139
217
166
606
Nintendo GameCube
55
92
83
88
318
Sega Dreamcast Totals
51
253
113
449
169
717
136
571
469
2000
11. The participant prefers the Sony PlayStation 2 system.
12. The participant prefers the Microsoft Xbox, given that the person is between the age of 13 and 18.
13. The participant prefers Nintendo GameCube, given that the person is between the ages of 13 and 24.
14. The participant is between 0 and 12 years of age, given that the person prefers the Sega Dreamcast
machine.
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.
16. A pair of dice are tossed. Find the probability that the sum on the two dice is 12, given that
doubles are rolled.
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?
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?
Remember: 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) ∙ 𝑃(𝐵)
19. What is the probability of drawing two cards in succession (without replacement) from a
standard deck and having them both be face cards?
20. Two cards are drawn from a standard deck without re- placement. Find the probability that both
cards are hearts.
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?
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?
In Exercises 23-26, 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.
23. Determine the probability that the first candy drawn is blue, the second is red, and the third is green.
24. Determine the probability that the first candy drawn is brown, the second is orange, and the third is
yellow.
25. What is the probability that the first two candies drawn are green and the third is red?
26. What is the probability that the first candy drawn is orange, the second is blue, and the third is orange?
In Exercises 27-30, three cards are dealt from a shuffled standard deck of playing cards.
27. Find the probability that the first card dealt is red, the second is black, and the third is red.
28. Find the probability that the first two cards dealt are clubs and the third is a spade.
29. 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.)
30. What is the probability that the three cards dealt are, in order, a red card, a club, and another
red card?