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Review Problems for Ch14/15 Quiz:
1. Are the events mutually exclusive?
 Roll two dice: sum is 6; doubles
 Randomly select a student at MHS: student is a freshman; student is in AP Calculus BC
 Randomly select a student at MHS: student takes English; student is in the Band
 Roll one die: a prime number; an even number
 Roll one die: an odd number; a number divisible by 3
 Roll two dice: 6 on one die; sum is 5
2. Are the events independent?
 Roll one die and then flip a coin
 Roll one die 3 times
 Pick a card from a deck, do NOT put it back, and then pick another card
 Pick a card from a deck, put it back, and then pick another
3. If you roll two dice, find …
a. P(a sum of 9)
f. P(a sum of 8 and doubles)
b. P(doubles)
g. P(a sum of 8 | doubles)
c. P(a sum of 9 or doubles)
h. P(a sum of 9 | doubles)
d. P(a sum of 8 or doubles)
i. P(doubles | a sum of 8)
e. P(a sum of 9 and doubles)
4. Roll a single die 3 times. Find…
a. P(all rolls are even numbers)
b. P(none are greater than or equal to 3)
c. P(at least one number is a multiple of 3)
d. P(the first 5 you get is on the third roll)
5. According to the Masterfoods company, the distribution of colors for M&M Mini’s is:
25% blue, 25% orange, 12% green, 13% yellow, 12% red, and the rest are brown.
a. If you pick an M&M Mini at random, what is the probability that…
i. it is brown?
ii. a primary color (red, yellow, blue)?
iii. it is not orange?
b) If you pick three M&M Mini’s in a row, what is the probability that…
i. they are all yellow?
ii. none are red?
iii. at least one is blue?
iv. the third one is the first one that is brown?
6. Suppose you pick three cards in a row at random from a standard deck of 52 cards, without
replacement. What is the probability that …
i. you get all jacks?
ii. you get no clubs?
iii. you get at least one red card?
7. There are a total of 2.4 million drivers in the United States who own two-seater sports cars. Of them, 1.8 million
are male, 2.1 million are single, and 1.6 million are male and single. Construct an appropriate diagram or table
and then answer the questions below.
What is the probability that a randomly selected driver of a two-seater sports car is…
a. male, but not single?
b. female?
c. male or single?
8. A survey of families revealed that 58% of all families eat turkey at holiday meals, 44% eat ham, and
16% have both turkey and ham to eat at holiday meals.
Make an appropriate diagram or table to represent the information above and then answer the
questions.
a. What is the probability that a family selected at random had neither turkey nor ham at their holiday
meal?
b. What is the probability that a family selected at random had ham but not turkey at their holiday meal?
c. What is the probability that a randomly selected family that had turkey at their holiday meal also had
ham?
d. Are having turkey and having ham disjoint events? Explain in context.
9.
For purposes of making on-campus housing assignments, a college classifies its students as Priority A
(seniors), Priority B (juniors), and priority C (freshmen and sophomores). Of the students who choose to
live on campus, 10% are seniors, 20% are juniors, and the rest are underclassmen. The most desirable
dorm is the newly constructed Gold dorm, and 60% of the seniors living on campus elect to live there. Of
the juniors living on campus, 15% of them live in the Gold dorm, along with only 5% of the on campus
underclassmen. What is the probability that a randomly selected resident of the Gold dorm is a senior?
Clearly show work to justify your answer.
10.
11.
ANSWERS:
1.
no
2.
yes
yes
yes
no
no
no
yes
no
yes
3.
a. 4/36
f. 1/36
b. 6/36
g. 1/6
c. 10/36
h. 0
d. 10/36
i. 1/5
e. 0
4.
a. (1/2)(1/2)(1/2) = 1/8
b. (2/6)(2/6)(2/6) = 8/216 = 1/27
c. 1 - P(no mult of 3's)
= 1 - (4/6)(4/6)(4/6) = 19/27
d. (5/6)(5/6)(1/6) = 25/216
5.
a.
i. .13
ii. .12 + .13 + .25 = .5
iii. 1 - .25 = .75
b.
i. (.13)(.13)(.13) = .002197
ii. (.88)(.88)(.88) = .681472
iii. 1 - P(none blue)
= 1 - (.75)(.75)(.75) = .578125
iv. (.87)(.87)(.13) = .098397
6.
i. (4/52)(3/51)(2/50) = .00018
ii. (39/52)(38/51)(37/50)= .41353
iii. 1 - P(no red cards)
1 - (26/52)(25/51)(24/50) = .88235
7. a. 0.2/2.4=.083
b. 0.6/2.4=.25
c. 2.3/2.4=.958
8. a.
b.
c.
d.
.14
.28
.16/.58=.2758
no.... 16% of
families had both turkey and ham
9.
10.
a.
b.
c.
43/223 = .143
113/223 = .507
15/223 = .067
11.
d.
a.
b.
141/223 = .632
(16/20)(15/19) = .6316
[not med , not med]
(16/20)(15/19)(4/18) = .1404
[not med, not med, med]