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Period _______
SECONDARY 2 ~ Lesson 11.2 Worksheet
Intro to Probability
Find the probabilities. Be sure to show how you set up the problem. Write each answer as a reduced
fraction.
Use the given information to complete problems 1 - 3.
Five students have the following locker combinations:
9–20–10
20–12–13
8–5–18
21–13–11
5–13–14
One of the combinations is chosen at random. Consider the following events.
E: The chosen combination contains an even integer.
grantee
F: The chosen combination contains a factor of 36.
unregenerate
1.
Draw a Venn diagram to show the sample space and the events E and F.
2.
Describe the following events by listing their outcomes.
𝐸𝐸 ∩ 𝐹𝐹
𝐸𝐸 ∪ 𝐹𝐹
3.
foresees
𝐹𝐹�
What is the probability that the chosen combination contains a factor of 36?
I
SECONDARY 2 ~ Lesson 11.2 Worksheet
Intro to Probability
Complement
:
elements
not
in
A
Name __________________________________
empty setiaset with no elements
Period _______
with
"
0
sets
Equal sets
a
the
Elements
same
Union ( AUB ) elements in A
intersection ( An B) elements
u
n
,
B,
or
both
in both
A
and
Find the probabilities. Be sure to show how you set up the problem. Write each answer as a reduced
fraction.
Pe
-:
t
Use the given information to complete problems 1 - 3.
Five students have the following locker combinations:
9–20–10
20–12–13
8–5–18
21–13–11
5–13–14
One of the combinations is chosen at random. Consider the following events.
E: The chosen combination contains an even integer.
F: The chosen combination contains a factor of 36.
1.
Draw a Venn diagram to show the sample space and the events E and F.
-
13¥
this
9-20-10
5-13-14
20-12-13
event
8-5
2.
Describe the following events by listing their outcomes.
𝐸𝐸 ∩ 𝐹𝐹
𝐸𝐸 ∪ 𝐹𝐹
elements In
{
E
elements
and F
both
{
9-20-10
8-5-18
3.
in
E ,F
,
or
𝐹𝐹�
both
20-12-13
{
8-
5.18
elements not
{
5-13.14
}
What is the probability that the chosen combination contains a factor of 36?
#
3
It
3/5
of
combinations
total # of possible
or
60%
with factors of
combos
36
int
5-13-14
21-13-11
q.zo.io
20-12-13
combination
doesn't
}
.
fit
in
either
4.
The following table shows a list of students and the extra-curricular activities in which they participate.
Consider these events:
C: the student is in Chess Club
D: the student is in Debate Club
B: the student is in Band
G: the student is in German Club
Describe the following events by listing their outcomes:
𝐶𝐶 ∩ 𝐺𝐺
𝐷𝐷 ∪ 𝐵𝐵
𝐵𝐵�
!i¥i¥¥±¥MI
Witt
"
¥
5.
Show the sample space for rolling a pair of dice.
.ee#ItHmIg?aw%aEF:maHi?IaaiaaqEeI&.eiei*e:*.ran.
6.
What is the probability that you will get a sum of 7 when you roll a pair of dice?
.mn#36ttM%abKutoIsTHgEEkFnEon
adf.yym.to#vgh%ce.2t53t4i4t3.5t2i6tzEMTq
irifferent
7.
combinations
that
How many ways can you roll a pair of dice and get an even product?
'll
"¥¥¥E¥!l¥¥I¥
,¥q
away
8.
Using your information from #7, what is the probability that you will get an even product when you roll
a pair of dice?
"
9.
Vick is playing a board game. To find the number of spaces to move, he rolls a pair of dice. What is the
probability that Vick rolls doubles or a sum of 2?
probate
10.
Ladarius is playing a board game. To find the number of spaces to move, he rolls a pair of dice. What is
the probability the he will roll doubles or a sum of 7?
.ba#e%a1agiE?isGjafmg:bgbwmEYt*MeFItfHtaE?Ionn%1e?EHH
"÷Ika
TIE
't
a
b
.
11.
The following Venn diagram shows a relationship between favorite sport and gender. Use it to answer
the following questions.
a.
How many people said soccer is their favorite sport?
35
b.
+50
85
=
How many females liked baseball?
none
c.
How many males chose soccer?
35
d.
What is the probability that a randomly chosen person will choose soccer as their favorite sport?
's
k$81
# of people
like soccer
who
85
#
141
60%
or
,
t can't be reduced
# Of peoples
Suppose you have a spinner that is divided into 3 equal pieces. One piece is yellow, one is red, and one
is blue. You will spin the spinner 2 times.
total
12.
a)
Sketch a tree diagram showing all of the possible outcomes when spinning the spinner 2 times.
red
red
1
Yellow
blue
red
Yellow
yellow
blue
red
blue
yellow
blue
b)
2
3
4
5
6
7
8
9
9 possible
outcomes
in total
What is the probability of spinning a red and then a blue?
1-
q
c)
What is the probability of spinning the same color on both spins?
:
d)
's
Think! If you know that you got the same color twice, what is the probability that the color was
red?
Color twice tz
the Same
probability of
:
getting
probability That the
So
-
in the 43
chance
that
you
the
get
43.113
Color Was
same
=
red
:
¥
#
of
color twice
,
you have
Yq
possible
colors
another 113
-
red , yellow ,
chance that
or
the
blue
color is red
13.
Nasir tosses a coin 3 times. Draw a tree diagram representing this situation. What is the probability that
HZ #
he gets at least 2 tails? Ftiptfl
:
58
tgeoftatneesas
HEADS
.YYYaniis
T
# of possible
14.
't
or
outcomes
At least 2 tails
Tang
4
:
HTITHTTTHTTT
James rolls a die 3 times. Draw a tree diagram representing this situation. What is the probability that
he will roll at least 2 even numbers?
7
108
zT6
tz
OR
g
ftp.t#tomtf3hgzf.pebto3-egngnefEgznfi
50%
28%
50%
28%
27
27
.
9
The table below lists items in Bryan’s closet. Use the table to answer questions 15-18.
gg3gmo--3oes8segsaasegs-fmemoozeffeeq
Combination
total
5
Clothing
4
3
15.
1
21
2
Bryan randomly selects 2 items from his closet. What is the probability that he selects 2 pairs of pants?
-5
chose from
toPants
# ofwaystopiokzpan ,
:
¥s÷µ¥b
# ofwayslopickzitms
16.
:
or
p(
shirt ) Eg
.4y }0z
seiedihgpantstpelectinga
43I=sz
Esor
÷zors%
Bryan randomly selects 2 items. What is the probability that both selected items are black?
combination
18.
Fs
Bryan randomly selects 2 items from his closet. What is the probability that he selects a pair of pants
then selects a shirt (without replacing the pants)?
permutation
17.
options
-
ttzoofewwatgsnaothstsetmywknsiton
C
(
9,2
)
Bryan randomly selects a pair of pants, then randomly selects a shirt. What is the probability that both
items are white?
PC selecting white
selecting white shirt )
pants
permutation
r
Stott
-
)•p(
Yzo
or
5%
.
Use this information for 19-20. Remember to write your answers as reduced fractions:
A bag of marbles contains 5 blue, 3 white, and 7 red marbles. You are going to draw two marbles. Find the
following probabilities.
15 marbles total
19.
You will draw a blue marble, replace it, then draw a red marble.
PC
Permutation
20.
drawing
a
blue marble )
.P( drawing
a
red marble)
.EE#ke7FsoR
↳fE
16%
You will draw a white marble, keep it, then draw another white marble.
P( white
Permutation
marble )
↳
21.
d
.pl
while marble)
¥5
Gtgoredyoe
3%
or
Fs .TT#ptonemarbleout
You are dealt a hand of three cards from a standard deck of 52 cards. What is the probability that you
there are 13 heart
will draw three hearts?
}
Pkk
Cards in each
deck
(
#0fWaysHPI9i3 hearts
c#,3)
combination
22.
# of ways Hpiok 3 Cards
zs6
gfto
#
452,3 )
l%
OR
Jack chooses a card from a standard deck of 52 cards, returns it to the deck, and the deck is shuffled. He
then chooses a card again. What is the probability that Jack will choose an Ace both times?
Yfoyr if
Pkhosinganace
§
)
.
PC (
)
?
.4€=
23.
anace
hosing
0.6%
or
There are 3 quarters, 4 dimes, and 5 nickels in a purse. Suppose 3 coins are to be selected without
replacement. 12 Mal
3piHaYtFX2f*wMe9uwaMY
a)
P(selecting 3 quarters) =
33
.
Combination
b)
.
-
Plpiauhgaquaner )
.pl
E. 't
Pain games 45
:
game )
zHo 0.5%
OR
picking
a
dime)
.P( nickel )
.TT#ztore7uutzoR
5%
2
5
The probability that your team wins a basketball game is . What is the probability that you will lose
the first 4 games?
P( lose
_
P(selecting a quarter, a dime, and then a nickel)=
permutation
24.
) pick
C(
3 quarters
Ways Hehose
# of ways toohose 3 coins
#K
:
315
Permutation
040.40%
or
or
0.6
or
60%
0.6×0.6×0.6×0.6=0.13
Chance
of losing
garnett
Chance
oil
,
losing
9ame#2
Chance
of losing
#3
chance
of
losing
#4
OR
g
,
gzz
ok
13%
P (a
25.
b) =P (a) tP( b)
0k
P(a
-
AND
this
b) quse
equation
Consuela is playing a card game with a standard 52-card deck. She wants a king or a diamond on her
first draw. What is the probability that she will get a king or a diamond on the first draw?
A
PC getting
a
King
4152
)
pldiamondj
:
p ( King
&
diamond)
:
HE -5¥
¥2
13152
b
=
For
31%
1/52
26.
240
142
Middletown High School has 240 students in the tenth grade. The only tenth grade math courses are
algebra and geometry. All of the tenth grade students are taking at least one math course. There are
142 students taking algebra and 120 students taking geometry. What is the probability that a randomly
chosen student is taking both algebra and geometry?
22
or
P( algebra + geometry
9%
students are in math
+120
algebra xudents
262-240
22
=
27.
:#
geometry students
Students
are
enrolled
=
hot
)
262 students
In both
in
math
Classes
Giada tosses a coin 3 times. What is the probability that she gets at least 2 consecutive heads or at least
2 consecutive tails?
a
Nd 0k b) =P (a) +P( b) p(q AND b)
b
-
my
µ ,
THH
HTT
PK Consecutive heads
)
HHH
TTT
p( 2 consecutive tails )
3g -0g
=
kg
24
ok
75%
3/8
:
P( both heads and tails )
Tt
318
:
:
%
Read the following scenario and use the information in it to complete problems 28-30.
A car dealership is having a contest. The first 10 customers to enter the contest are each given 2
raffle tickets. The remaining 20 customers are each given 1 raffle ticket. There is 1 contest
winner, selected by randomly choosing one of the raffle tickets.
total
28.
#
of
tickets given out :C 10.2 )
+20=40
Spencer is one of the first 10 customers to enter the contest. What is the probability that he will win the
raffle?
2spehtchfkhkas
total
40
-
tt of tickets
Yet
or
5%
29.
Hope is one of the remaining 20 customers to enter the contest. What is the probability that she will win
the raffle? Hope has one
or
3%
Hot
ticket Out of go
30.
Is the game fair? Explain.
yes
is
of
its
minimal
that the first 10
advantage
Increase
in
They only have a 2%
because
fair
.
winning
.
the
customers
have
their chance
25.
Consuela is playing a card game with a standard 52-card deck. She wants a king or a diamond on her
first draw. What is the probability that she will get a king or a diamond on the first draw?
26.
Middletown High School has 240 students in the tenth grade. The only tenth grade math courses are
algebra and geometry. All of the tenth grade students are taking at least one math course. There are
142 students taking algebra and 120 students taking geometry. What is the probability that a randomly
chosen student is taking both algebra and geometry?
27.
Giada tosses a coin 3 times. What is the probability that she gets at least 2 consecutive heads or at least
2 consecutive tails?
.ee/oIeekz.#rr....mai.*ffEdoeaYeaeEkbghY..r
Read the following scenario and use the information in it to complete problems 28-30.
A car dealership is having a contest. The first 10 customers to enter the contest are each given 2
raffle tickets. The remaining 20 customers are each given 1 raffle ticket. There is 1 contest
winner, selected by randomly choosing one of the raffle tickets.
28.
Spencer is one of the first 10 customers to enter the contest. What is the probability that he will win the
raffle?
29.
Hope is one of the remaining 20 customers to enter the contest. What is the probability that she will win
the raffle?
30.
Is the game fair? Explain.