Download REVIEW for EXAM

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REVIEW for EXAM
Directions: Read and solve each question. Be sure to show your work. NO WORK = NO CREDIT
Sample Space
Sample Space
QUESTION
Things to remember…
Sample Space shows all the possible outcomes of
an event. The sample space can be shown as a
TREE DIAGRAM or LIST.
Example: Show the sample space for spinning
the spinner and picking a marble.
1
9
There are 2 red marbles, 2 yellow marbles, and 1
purple marble in a bag. Sam picks 2 marbles
from the bag. Which list shows all the possible
unique outcomes?
A
Purple/red, purple/yellow, yellow/red,
yellow/yellow, red/red
B
Purple/purple, purple/red, purple/yellow,
yellow/red, yellow/yellow, red/red
C
Yellow/red, yellow/yellow, yellow/purple
3
7
5
D Purple/red, purple/yellow, yellow/red,
yellow/purple, red/yellow, red/purple
TREE DIAGRAM
Spinner
1
3
5
7
9
LIST
Marble
1,
1,
1,
1,
1,
White
Grey
Striped
Spotted
Black
3,
3,
3,
3,
3,
White
Grey
Striped
Spotted
Black
Things to remember…
5,
5,
5,
5,
5,
White
Grey
Striped
Spotted
Black
The fraction form is
White
Grey
Striped
Spotted
Black
7,
7,
7,
7,
7,
White
Grey
Striped
Spotted
Black
White
Grey
Striped
Spotted
Black
9,
9,
9,
9,
9,
White
Grey
Striped
Spotted
Black
White
Grey
Striped
Spotted
Black
White
Grey
Striped
Spotted
Black
White
Grey
Striped
Spotted
Black
To determine the total possible outcomes…
 Count the combinations in the tree diagram
 Count the combinations in the list
 Use the Counting Principle…
# of outcomes Event 1
x
# of outcomes Event 2
5 x 5 = 25 total outcomes
Probability and its Complement
The probability of any event can be written as a
fraction, decimal, or percent.
Favorable outcomes
Total outcomes
The COMPLEMENT of any event is what is NOT
included
P(EVENT) + P(COMPLEMENT) = 1
Example: Find the probability of spinning blue
and its complement.
blue
green
red
purple
yellow
P(blue)
P(NOT blue)
COMPLEMENT
EVENT
1
5
+
4
5
=
5
5 or
1
Probability and its Complement
QUESTION
Which of the following correctly describes the
relationship between the probability of rolling a 2
and the probability of its complement on a
standard six-sided number cube?
INDEPENDENT Example 2:
Find the probability of picking two vowels, if you
pick one card, replace it, then pick a second card.
E
X
A
M W
D
E
N
E
S
D
A
Y
P(vowel, vowel)
5
5
25
x
=
13
13
169
A
The probabilities are equal.
B
The probabilities have a product of 1.
C
The probability of rolling a 2 is
, and the
probability of not rolling a 2 is
.
DEPENDENT Example:
Find the probability of picking two striped
marbles, if you pick one, then without replacing
it, picking another.
D The probability of rolling a 2 is less than the
probability of not rolling a 2.
P(striped, striped)
3
2
6
x
=
90
10
9
Compound Events
Things to remember…
There are two types of compound events:
 Independent (replacing or separate events)
o Find the probability of each event, then
Compound Events
QUESTION
MULTIPLY
 Dependent (WITHOUT replacing)
o Find the probability of each event, then
MULTIPLY
INDEPENDENT Example 1:
Mary had a stack of 10 cards numbered 1-10.
She randomly chooses two cards without
replacing the first card. What is the probability
that Mary chooses two composite numbers?
Find the probability of flipping tails, spinning red,
and picking a striped marble.
A
red
blue
B
2
9
1
4
because
because
5
10
5
10
4
∙
=
9
5
∙
10
=
20
90
25
100
yellow
C
P(tails, red, striped)
1 x 1 x 2
= 2
3
75
5
5
D
1
5
because
5
18
5
10
because
5
10
4
∙
10
∙
5
9
=
=
20
100
25
90
Theoretical & Experimental
Predictions
Things to remember…
Things to remember…
 Theoretical Probability – what SHOULD
happen; normal probability
 Experimental Probability – what ACTUALLY
happens; probability based on DATA
To make a prediction using probability you must
use a PROPORTION.
Example:
Jaylen rolled a fair number cube 100 times. He
recorded his results below.
Theoretical Probability
QUESTION
Noah has five cartons of orange juice, three
cartons of apple juice, and two cartons of
cranberry juice in his refrigerator. He takes out a
carton at random and then another one without
replacing the first. What is the theoretical
probability that both cartons are of orange juice?
Number
on die
1
2
3
4
5
6
Times
rolled
11
27
18
23
9
12
A
If Jaylen rolls the die 250 times, about how many
times should he expect to roll a 2 or 3?
B
First, find experimental probability.
P(2 or 3)
45
100
C
D
Second, set up and solve a proportion.
45 = x
100
250
Experimental Probability
QUESTION
This is not a real question. You must keep
reading and follow the directions. On a separate
sheet of paper, you must write a note to your
teacher listing the answer choices from greatest
to least. If you turn it in before your exam, you
may receive some extra credit points.
A
250
B
125
C
200
D
375
45 x 250 = 11250
11250 ÷ 100 = 112.5
Jaylen should roll a 2 or 3 about 113 times.
Predictions
QUESTION
Qualitative and Quantitative
Things to remember…
Aisha helps her mother at the family store. She
has to decide how many of each kind of package
of battery to sell in the store next week. The
table shows how many packages of each kind of
battery were sold yesterday.
Qualitative data is information about
QUALITITIES. This data canNOT be measured
using numbers.
Example: less likely, more likely, impossible
Quantitative data is information about
QUANTITIES. This data can be measured using
numbers.
Example: 54 inches, 12 feet, 33 days
If Aisha's mother says to order 50 packages of
batteries, how many packages of AA batteries
should Aisha order?
Qualitative and Quantitative
QUESTION
A bag contains only red and blue marbles.
A
12

There are 6 marbles in the bag.
B
13

The bag contains twice as many blue
C
24
D
25
marbles as red marbles.
Nadia draws a marble and replaces it. She
repeats this process 18 times. What is the best
prediction of the number times Nadia will draw a
blue marble?
A
4 times
B
6 times
C
10 times
D
12 times