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Math Problems
Grade 8
Probability of simple events
6
6
6
. Henty bought an electric guitar which was advertised at
$
1280
\$ 1280
$1280
excluding GST. If the
\newline
(b) the price of the guitar inclusive of GST.
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Lin and Kai are friends that work together on a team of
n
n
n
total people. Their manager is going to randomly select
2
2
2
people from the team of
n
n
n
to attend a conference. What is the probability that Lin and Kai are the
2
2
2
people chosen? Choose
1
1
1
answer:
\newline
(Choice A)
1
(
n
2
)
\frac{1}{\binom{n}{2}}
(
2
n
)
1
\newline
(Choice B)
(
n
2
)
\binom{n}{2}
(
2
n
)
\newline
(Choice C)
2
n
\frac{2}{n}
n
2
\newline
(Choice D)
2
n
(
n
−
1
)
\frac{2}{n(n-1)}
n
(
n
−
1
)
2
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In an
8
8
8
-minute long game, a professional video game player performed a total of
2
,
400
2,400
2
,
400
actions. What is the player's average number of actions per minute?
\newline
Choose
1
1
1
answer:
\newline
(A)
30
30
30
\newline
(B)
160
160
160
\newline
(C)
300
300
300
\newline
(D)
400
400
400
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S/
1521701
1521701
1521701
/quizzes/
3654992
3654992
3654992
/take
\newline
Question
1
1
1
\newline
1
1
1
pts
\newline
Suppose the spinner shown below is spun one time. What is the probability that the pointer will land on
1
1
1
or
2
2
2
?
\newline
3
3
3
\newline
2
5
\frac{2}{5}
5
2
\newline
1
3
\frac{1}{3}
3
1
\newline
1
2
\frac{1}{2}
2
1
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You've decided you want a plant for your room. At the gardening store, there are
4
4
4
different kinds of plants (tulip, fern, cactus, and ficus) and
4
4
4
different kinds of pots to hold the plants (clay pot, plastic pot, metal pot, and wood pot).
\newline
If you randomly pick the plant and the pot, what is the probability that you'll end up with a tulip in a plastic pot?
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You're at a clothing store that dyes your clothes while you wait. You get to pick from
4
4
4
pieces of clothing (shirt, pants, socks, or hat) and
3
3
3
colors (purple, blue, or orange).
\newline
If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with an orange hat?
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You're playing a game where you defend your village from an orc invasion. There are
3
3
3
characters (elf, hobbit, or human) and
5
5
5
defense tools (magic, sword, shield, slingshot, or umbrella) to pick from.
\newline
If you randomly choose your character and tool, what is the probability that you'll be a magic elf?
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You're at a clothing store that dyes your clothes while you wait. You get to pick from
4
4
4
pieces of clothing (shirt, pants, socks, or hat) and
3
3
3
colors (purple, blue, or orange).
\newline
If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with socks that aren't blue?
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There are
10
10
10
people on a basketball team, and the coach needs to choose
5
5
5
to put into a game. How many different possible ways can the coach choose a team of
5
5
5
if each person has an equal chance of being selected?
\newline
Answer:
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You flip a coin.
\newline
What is
P
(
tails
)
P(\text{tails})
P
(
tails
)
?
\newline
Write your answer as a percentage.
\newline
_
_
_
_
%
\_\_\_\_\%
____%
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Mariam invests money in an account paying simple interest. She invests
$
160
\$ 160
$160
and no money is added or removed from the investment. After one year, she has
$
166.40
\$ 166.40
$166.40
. What is the simple percent interest per year?
\newline
Answer: _________
%
\%
%
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Taub has a loyalty card good for a discount at her local grocery store. The item she wants to buy is priced at
$
32
\$ 32
$32
, before discount and tax. After the discount, and before tax, the price is
$
29.12
\$ 29.12
$29.12
. Find the percent discount.
\newline
Answer: _____
%
\%
%
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Adriel invests money in an account paying simple interest. He invests
$
150
\$ 150
$150
and no money is added or removed from the investment. After one year, he has
$
159
\$ 159
$159
. What is the simple percent interest per year?
\newline
Answer: __________
%
\%
%
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Malik invests money in an account paying simple interest. He invests
$
30
\$ 30
$30
and no money is added or removed from the investment. After one year, he has
$
30
\$ 30
$30
.
30
30
30
. What is the simple percent interest per year?
\newline
Answer: ______
%
\%
%
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Myesha rolls a standard six-sided die, numbered from
1
1
1
to
6
6
6
. Which word or phrase describes the probability that she will roll a
1
1
1
?
\newline
an equal chance or
50
50
50
−
50
-50
−
50
\newline
unlikely
\newline
certain
\newline
likely
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A multiple choice exam consists of
30
30
30
multiple choice questions, with
5
5
5
possible answers per question. Assuming that you randomly select an answer for each question, what is the probability that you get exactly
15
15
15
,
16
16
16
, or
17
17
17
questions correct?
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The stock of Company A gained
$
1.30
\$ 1.30
$1.30
throughout the day and ended at a value of
$
53.30
\$ 53.30
$53.30
. By what percentage did the stock rise?
\newline
Answer:
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The stock of Company A gained \$\(0\).\(21\) throughout the day and ended at a value of \( \$ 3.71 \). By what percentage did the stock rise?\(\newline\)Answer:
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The stock of Company A lost
$
4.86
\$ 4.86
$4.86
throughout the day and ended at a value of
$
103.14
\$ 103.14
$103.14
. By what percentage did the stock decline?
\newline
Answer:
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A clothing warehouse that houses
14
,
000
14,000
14
,
000
garments must replace all damaged and lost garments. If
1.5
%
1.5\%
1.5%
of the garments were damaged and
0.6
%
0.6\%
0.6%
of the garments were lost, how many garments must the warehouse replace?
\newline
Choose
1
1
1
answer:
\newline
(A)
84
84
84
\newline
(B)
126
126
126
\newline
(C)
210
210
210
\newline
(D)
294
294
294
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In
2019
2019
2019
, the population of the City of Detroit was approximately
670
670
670
thousand. The land area of the City of Detroit is approximately
138.7
138.7
138.7
square miles. Which of the following is closest to the population density of the City of Detroit in
2019
2019
2019
in people per square mile of land area?
\newline
Choose
1
1
1
answer:
\newline
(A)
5
5
5
\newline
(B)
207
207
207
\newline
(C)
4
,
831
4,831
4
,
831
\newline
(D)
92
,
929
92,929
92
,
929
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In an
8
8
8
-minute long game, a professional video game player performed a total of
2
,
400
2,400
2
,
400
actions. What is the player's average number of actions per minute?
\newline
Choose
1
1
1
answer:
\newline
(A)
30
30
30
\newline
(B)
160
160
160
\newline
(C)
300
300
300
\newline
(D)
400
400
400
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Nia is
1
1
1
of
24
24
24
students in a class. Every month, Nia's teacher randomly selects
4
4
4
students from their class to act as class president, vice president, secretary, and treasurer. No one student can hold two positions.
\newline
In a given month, what is the probability that Nia is chosen as president?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
24
P
4
\frac{1}{{ }_{24} \mathrm{P}_{4}}
24
P
4
1
\newline
(B)
1
24
C
4
\frac{1}{{ }_{24} \mathrm{C}_{4}}
24
C
4
1
\newline
(C)
23
P
3
24
P
4
\frac{{ }_{23} \mathrm{P}_{3}}{{ }_{24} \mathrm{P}_{4}}
24
P
4
23
P
3
\newline
(D)
(
24
P
1
)
⋅
(
24
P
3
)
24
P
4
\frac{\left({ }_{24} \mathbf{P}_{1}\right) \cdot\left({ }_{24} \mathrm{P}_{3}\right)}{{ }_{24} \mathrm{P}_{4}}
24
P
4
(
24
P
1
)
⋅
(
24
P
3
)
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A circus has
15
15
15
performers, of which
5
5
5
are clowns.
\newline
What is the probability that a randomly selected performer will be a clown? Write your answer as a fraction or whole number.
\newline
P
(
clown
)
=
P(\text{clown}) =
P
(
clown
)
=
______
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