Mathematics 1228A/B Study Guide - Final Guide: List Of Poker Hand Categories, Bernoulli Trial, Sample Space

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Friday, April 21,2006
Page 1 CODE 111 Mathematics 028b
Final Examination
1. There are 2 reddisks, 1greendisk and 3 black disks in a bag. Frank is going to draw disks
from the bag, one at a time, withoutreplacement, until he finds a black disk. (Assoon as
he draws a black disk, Frank will stopdrawing disks from the bag.) How many dierent
colour sequences are possible? (For instance, “black firsttry”, “draw red then green then
black”and “draw green then red thenblack”are 3of the possiblecolour sequences of
Frank’s draws.)
A: 3 B: 5 C: 9 D:13
2. Considerthecounting tree shownhere:
43!A
"B
8#C
#
Cc
"
16Bc
#C
#
5Cc
!
Ac
"B
#C
#
12Cc
"
Bc13#C
#
Cc
If it is known that n(C) = 45,find n(B).
A:52 B:43 C:27 D: cannot be determined
3. Joanne has 4 dierent paperback books and 3 dierent hardcover books to put on a book-
shelf. Inhow many distinct ways can the books be arranged if she wants to put all the
paperbacks together and all the hardcover books together?
A: 7! B:7!
3!4! C: 3!4! D: 3!4!2!
4. Nine friendsgo intoamovie theatre. They cannot find 9 seats together, butthey do find
agroup of 5 seats in a row and 4 seats in the row directly behind. Inhow many ways can
the 9 friends arrange themselves in these seats?
A: 9! B:9!
4! ×5! C:!9
5"×4! D:9!
4!5!
5. Inhow many distinct ways can 6 kindergarten children, 1 teacher and 1 teacher’s aide
arrange themselves in a circle?
A: 8! B: 7! C: 6! D: 5!
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Mathematics 028b
Final Examination CODE 111 Friday, April 21,2006
Page 2
6. Inhow many ways canSaddiq choose 8of his 20 Grade 1 classmates to invite to his
birthday party?
A:20!
8! B:20!
12!C:20!
8!12!D: 8
7. Inhow many distinct ways can the letters of the word ABRACADABRA be arranged?
A: 211 B:11!C:!11
52112
"÷(2!2!) D:!11
52112
"
8. Seventeen students are going to Hamilton to see a Ti-Cats football game. Sue and Ed will
drive their own cars, and Joe has arranged to drive his parents’ minivan. The minivan
holds 7 people, Sue’s car can carry 5, and Ed’s only holds 4. Bill isgoing to ride alone on
his motorcycle. Inhow many dierent ways can the others decide which vehicle to travel
in?
A:133B:!13
643
"C:174D:!17
7541
"
9. The following week, 16 of the students are going to Toronto to see a Blue Jays baseball
game. The students have decided to travelin2groups of 5and agroup of 6. One member
of each group wouldbe responsible for organizing transportation forthat group. Inhow
many dierent ways can transportation organizers bechosen and the students assigned to
the groups?
A:16!
6!5!5! B:16!
6!5!5!2! C:16!
5!4!4! D:16!
5!4!4!2!
10. Martha has hidden 15 identical easter eggsso that her 3 children canhave an easter egg
hunt. If all eggs are found during the hunt,inhow many dierent ways could theeggs be
distributed among thechildren when it’s over?
A:!17
15"B:!17
3"C:!15
3"D: 315
11. Referto question 10. If some of theeggs might not be found,inhow many ways could
eggs be distributed among thechildren aftertheeaster egg hunt?
A:154B:!17
15"C:!18
15"D:15 ×14 ×13 ×12
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Friday, April 21,2006
Page 3 CODE 111 Mathematics 028b
Final Examination
12. If Pr[A] = .6, Pr[B] = .5and Pr[AB] = .9, what is Pr[AB]?
A:.1B:.2C:.3D:.03
13. Let S={a, b, c, d}be a sample space for someexperiment. If E={a, b}with Pr[E] = .4
and it is known that Pr[d] = 3Pr[c], what is Pr[c]?
A:.15 B:.2C:.25 D:.3
14.Suppose that Aand Bare 2 mutually exclusiveevents defined on the same sample space.
If Pr[A] = .3and Pr[AcBc] = .2, what is Pr[B]?
A:.8B:.7C:.5D: cannot be determined
15. Aunt Eloise is visiting her 3 nephews for Christmas. She has 6 dierent small toys and
she is going to put 2 in eachboy’sstocking. She doesn’t knowwhich stocking belongs to
whichboy, so she distributes the toys randomly. What is the probability that Freddy gets
both the tiger and the fire truck and Carl gets the yoyo?
A:33
36B:1
36C:3!
!6
222
"D:3
!6
222
"
16. If 6 children arrive at schoolin random ordertomorrow morning, what is the probability
that Benji and Sally(twoof the 6 children) arrive one-after-the-other?
A:1
3B:1
6C:1
60 D:1
720
17. A 5-cardpoker hand is dealt atrandom from a standarddeck. What is the probability
thatthe hand is a flush,i.e., all 5 cards are the same suit?
A:1
45B:4
45C:!13
5"
!52
5"D:!4
1"!13
5"
!52
5"
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