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

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Published on 2 Aug 2020

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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 diﬀerent

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

"

❍

16❍Bc

#C

#

❳

5❳Cc

!

❅❅Ac

"B

#C

#

❳

12❳Cc

"

❍❍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 diﬀerent paperback books and 3 diﬀerent 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!

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 diﬀerent 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 diﬀerent 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 diﬀerent 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

Friday, April 21,2006

Page 3 CODE 111 Mathematics 028b

Final Examination

12. If Pr[A] = .6, Pr[B] = .5and Pr[A∪B] = .9, what is Pr[A∩B]?

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[Ac∩Bc] = .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 diﬀerent 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"