Math 112A Probability Rewrite Assignment - 2009
MacMillan/ Manuel
/31
Name:_______________
Part I. Multiple Choice. Choose the best answer and place it in the corresponding blank at the end. (value 15)
1. Suppose you do not replace the 1st card before selecting a 2nd from a well-shuffled deck. Which is used to find the probability that the
outcome will be two black face cards?
a) 12  11
b) 6  5
c) 6  6
d) 6  6
52 51
52 51
52 52
52 52
2. The value 5! is equivalent to:
a) 5P1
b) 5P5
c) 5C5
d) 5C1
3. Which can be used to find how many different license plate numbers are possible in the form "letter, number, letter, number, letter,
number" if the first letter cannot be an A, the number 0 is not possible and no letter or number can be repeated?
a) 25x9x24x8x23x7
b) 25x9x25x8x24x7
c) 25x10x25x9x24x8
d) 24x9x24x8x23x7
4. A multiple choice test has 12 questions with each question providing four choices for answers (A, B, C or D). How many different
sets of answers are possible for the test?
a) 16777216
b) 20736
c) 48
d) 479001600
5. What is the probability of selecting a ten or a red card from a well-shuffled deck of cards?
a) 15
b) 7
c) 15
d) 29
26
13
52
52
6. What is the probability of selecting an Ace or a red Queen from a well-shuffled deck of cards?
a) 3
b) 5
c) 3
d) 2
26
52
52
13
7. A red die and a blue die are tossed. What is the probability that the red die shows a three and the blue die shows a number greater than
three?
a)
1
36
b) 1
c) 1
d) 2
18
12
3
8. Which expression can be used to determine the number of permutations when arranging all the letters in the word “LETTERS”?
a) 7!
b) 7!
c) 7!
d) 7!
2!
4!
2!2!
9. A committee of three is randomly selected from a group of 4 males and 5 females. Which can be used to determine the probability
that all males will be chosen?
3
4 C3
4 C3
1
a)
b)
c)
d)
C
C
C
4 3
9 3
9 3
9 C4
10. A bag contains 10 green and 4 blue marbles. Suppose you removed 2 marbles at random, without replacement. What is the
probability that the two marbles will be blue?
a) 4
b) 6
c) 7
d) 6
49
91
27
7
11. Which of the following represents the probability of Dan, Erin, and Jane placing first, second, and third (in that order) out of a group
of 8 runners?
1
1
1
a) 1
b)
c)
d)
8!
8 P5
8 C3
8 P3
12. There are 6 boys and 5 girls on a committee. Four members of the committee will be randomly selected to go to a conference.
Which of the following represents the probability that only 1 girl is selected to go to the conference?
a) 5C3 x 6C1
b) 6C3 x 5C1
c) 6C3 + 5C1
d) 6C3 x 5C1
11C4
11C3
11C4
11C4
13. Which of the following lists is the first 4 elements of the 16th row of Pascal’s Triangle?
a) 1 16 120 560
b) 1 16 120 240
c) 1 16 240 3360
d) 1 16 256 4096
14. Which of the following is equivalent to the first 4 terms of (x + 1)12 ?
a) x12 + 11x10 + 66x9 + 495x8
c) x12 + 12x11 + 66x10 + 220x9
12
11
10
9
b) x + 12x + 220x + 495x
d) x11 + 11x10 + 66x9 + 220x8
15. Which of the following is equivalent to x6 + 6x5y +15x4y2 + 20x3y3 + 15x2y4 + 6xy5 + y6 ?
a) (x + 1)6
b) (x + y)5
c) (x + y)6
d) (x + 1)y
Answers:
1. ______ 2. ______ 3. ______ 4. ______ 5. ______ 6. ______ 7. ______ 8.______
9.______ 10. ______11. _____ 12._____ 13._____ 14. ______ 15. ______
Part II. Open Response. Show work in the space provided to receive full value. (Value 16)
1. Complete the following Venn Diagram for a deck of cards.
Face
Cards
spades
_____
_______
2. Write the first four terms of the expanded form of (x + y) 16.
_____
____
_____
(value 2)
(value 2)
_____
3. Jessie and Paige are soccer players taking penalty kicks in a shootout. Jessie typically averages three out of every five shots while
Paige averages one out of every four. Construct an area model diagram for this situation and use it to determine the probability that Jessie
or Paige make their shots.
(value 3)
Area Model Diagram
4. What is the probability of selecting a Ten or a club from a standard deck of 52 cards?
(value 3)
5.
Consider the Scratch-and-Win ticket to the left:
IPod
DVD
DVD
DVD
IPod
DVD
Try
Again
IPod
DVD



you can scratch only three boxes
you must scratch three identical boxes to win a prize
two possible prizes to be won – an IPod or a DVD
Determine the probability of winning on this ticket.
(value 3)
6. A committee of 6 people is selected from a group of 8 females and 7 females. What is the probability that there are exactly four males
selected for the committee?
(value 3)