Download Algebra 2 - Chapter 11 Practice Test

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Algebra 2 - Chapter 11 Practice Test
1.
A box contains 3 green marbles, 3 yellow marbles, and 2 red marbles. All selections from
the box are totally random.
a. Suppose you select one marble. What is the probability that the marble will be yellow?
b. Suppose you select a marble, replace it (put it back into the box), and then select a
second marble. What is the probability that both marbles were yellow?
c. Suppose you select a marble and then without replacing it (you don’t put it back into
the box), you select a second marble. What is the probability that both marbles were
yellow?
d. Suppose you select two marbles (take out one marble and then without putting it back
into the box, take out a second marble). What is the probability that neither of the two
marbles was yellow?
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2.
Box #1 contains 2 green marbles, 3 yellow marbles, 3 red marbles.
Box #2 contains 3 green marbles, 2 yellow marbles, 2 red marbles.
a. Suppose you select one marble from each box. What is the probability that both
marbles will be green?
b. Suppose you select two marbles from each box. What is the probability that all four
marbles are yellow?
c. Suppose you select one marbles Box #1 and then place that marble in Box #2. Then
you select one marble from Box #2. What is the probability that both selections were a
green marble?
3.
An ice cream store has 15 different flavors of ice cream, 10 different toppings, and 3
different types of cones from which you can choose.
a. Suppose you ordered a single cone (one scoop of ice cream) with one topping. How
many different ways could you order your ice cream cone?
b. Suppose you ordered a double cone (two scoops of ice cream) with one topping. If the
two scoops are different flavors, how many different ways could you order?
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4.
A bookstore has a sale and you want to buy cookbooks. They have 12 cookbooks and you
decide to buy 3 of them. How many possible combinations could you choose from?
5.
A high school 400m track race has 7 students running in it. The school newspaper will
print the names of the three top winners (1st, 2nd and 3rd place) in that order. How many
possible ways can the three names be printed?
6.
A teacher has 12 students in the Math Club (yeah … as if you could find 12 students to join
a club like that?). The teacher needs to randomly choose 4 of the club members to visit
another school. How many possible combinations of students could the teacher choose?
7.
You have 6 different books and want to arrange all six of them on a shelf (side by side).
How many ways can you arrange them on the shelf?
8.
How many unique (different) ways can you order the letters in the word “UNIQUE”?
9.
How many unique (different) ways can you order the letters in the word “REORDER”?
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10.
A bag contains 7 red marbles, 5 blue marbles and 4 black marbles.
a.
If you randomly take out two marbles (at the same time), what is the probability that
both marbles are red?
b.
11.
If you randomly take out one marble, then put it back in the bag and then again take
out one marble, what is the probability that both selected marbles were black?
A penny is tossed 6 times.
a.
If you record the sequence of heads and tails as you toss the coin, how many different
sequences are possible?
b.
What is the probability of getting the sequence H-T-T-H-H-T in that exact order?
12.
The odds of winning in a card game are 5:6 (5-to-6).
winning?
13.
The probability of winning on a bet is
14.
The probability of losing on a bet is
What is the probability of
. What are the odds of winning?
. What are the odds of winning?
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15.
Suppose you randomly select two cards from a standard deck of cards. What is the
probability that both cards are the same suit?
16.
Suppose you randomly select two cards from a standard deck of cards. If both cards are
black, what is the probability that both cards are the same suit?
17.
Suppose you randomly select three cards from a standard deck of cards. What is the
probability that all three cards are red?
18.
If you randomly select three cards from a standard deck of cards and all three cards are face
cards, what is the probability that all three cards are Jacks?
19.
Suppose you shuffle a standard deck of cards and take the top ten cards from the deck. You
discard the other cards and you now are holding a stack of ten cards.
a. What is the probability that the Ace of Spades is one of the ten cards you’re holding?
b. What is the probability that the Ace of Spades is the top card in the ten-card stack you
are holding?
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20.
You roll two dice. What is the probability of getting a pair?
21.
You roll three dice. What is the probability that all three numbers are different?
22.
You roll two dice. What is the probability of rolling a sum of 9 or greater?
23.
You roll two dice and the sum is greater than “4”. What is the probability of rolling a sum
of 7?
24.
You roll two dice and neither one is a “5”. What’s the probability of rolling a sum of 7?
25.
You roll two dice and the sum is “10”. What is the probability that one of the dice is a 6?
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26.
Given S = { 4 , 7 , 3 , 7 , 4 , 9 , 3 , 1 , 7 }
a. What is the mean value?
b. What is the median value?
c. What is the mode?
27.
Suppose the number of “friends” that members have on Facebook is a normal distribution
with a mean of  = 640 and a standard deviation of  = 220.
a. Approximately what percentage of Facebook members have less than 200 friends?
b. Approximately what percentage of members has more than 860 friends?
c. Approximately what percentage of members has between than 420 and 1080 friends?
28.
Consider the following two distributions. Both have the same mean of  = 5:
{1 2 3 4 5 6 7 8 9}
{3 3 4 4 5 6 6 7 7}
Which one has a larger standard deviation  than the other? Why?
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TAKES A LITTLE MORE THINKING:
A)
There are two girls and two boys in a classroom. Two of them are randomly called to another
room. What is the probability that the two remaining students have the same gender?
B)
A donut shop offers three different types of muffins. You decide to buy four muffins. If the order
in which you list out the four muffins you want doesn’t matter, how many different ways can you
order four muffins?
C)
A survey shows that the average height of 8-year old boys is 56.25 inches with a standard
deviation of 1.25 inches. If you take the data and add 4 inches to each data point, what would the
mean and standard deviation be for your new data set?
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ANSWERS TO CHAPTER 11 PRACTICE TEST:
=
1-a:
1-b:
·
=
1-c:
·
=
=
1-d:
·
=
2-a:
·
=
=
2-b:
·
·
2-c:
·
=
=
=
·
3-a:
15 · 10 · 3 = 450
3-b:
4:
C(12,3) = 220
5: P(7,3) = 210
6:
C(12,4) = 495
7: P(7,7) = 7! = 5040
8:
6 letters, 2 U’s :
9:
7 letters, 2 E’s, 3 R’s :
10-a:
·
=
10-b:
·
=
11-a:
=
·
=
C(15,2) · 10 · 3 = 105 · 10 · 3 = 3150
= 420
=
=
·
=
…. And so odds are 4:3
…. And so odds are 3:8
=
·
·
= 360
=
·
·
· · · · ·
11-b:
=
(Winning is bolded)
=
14:
15:
=
·
2·2 ·2 ·2 ·2 ·2
12:
13:
=
=
=
=
(Winning is bolded)
(Winning is bolded)
16:
·
=
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17:
·
·
=
·
·
18:
·
·
=
·
·
=
=
·
·
19-a:
20:
·
·
=
·
·
=
=
(There are 12 faces cards in a deck)
19-b:
=
·
21:
·
·
=
=
22:
=
(Ten successes: 6-3, 5-4, 4-5, 3-6, 6-4, 5-5, 4-6, 6-5, 5-6, 6-6)
23:
=
(Conditional on 30 possible rolls)
24:
(Conditional on 25 possible rolls)
25:
(Success: 6-4, 4-6,
=
26-a:
Failure: 5-5 )
= 9
47779
26-b:
1 3 3 4
26-c:
1 3 3 4 4
27-a:
X ≤ –2standard deviations): 50% – 13.5% – 34% = 2.5%
27-b:
X ≥ +1: 50% – 34% = 16%
27-c:
–1 ≤ X ≤ +2:
28:
The first set has the larger standard deviation. The reason is that the numbers “vary” further away
from the “center” (mean).
A:
·
=
7 7 79
0–4
34% + 34% + 13.5% = 81.5%
(After the first student is chosen, only 1/3 remains to be the same gender leaving the room)
= 15
B:
5+4+3+2+1
C:
Mean:  = 56.25 + 4 = 60.25 ,
Standard Deviation:  = 1.25 (unchanged)
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