Download Sample Space name

Applications of Mathematics 12
Sample Space
sample space
name: ____________
A Sample space is __________________________________________________________________
There are many different ways to determine and show a sample space: pictures / diagrams (eg a bag of
marbles shown in a textbook), Venn Diagrams, Tree Diagrams, and Tables.
Probability Trees – show each trial of a simulation so that you can follow the
pathways to list the sample space. You can make them horizontally or vertically.
Try both until you find the way you prefer.
1. Determine the sample space for throwing 3 coins. Use a probability tree. Try horizontally.
a)
What is the probability that there will be 2 heads and 1 tail?
b)
What is the probability that there will be 3 heads?
c)
What is the probability that there will No heads?
d)
What is the connection between P(3 heads) and the P(no heads) ?
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Applications of Mathematics 12
sample space
EXAMPLE 2:
Determine the sample space for throwing a 4 sided dice followed by tossing a nickel followed by tossing
a dime. Use a probability tree. Try vertically.
2
(a)
What is the probability that there will be the number three on the dice and 2 heads?
(b)
What is the probability that there will be an even number followed by a head and a tail?
(c)
What is the probability that there will be the number 7 followed by 2 heads ?
(d)
What is the probability that there will be a number followed a tail then a head ?
Applications of Mathematics 12
Sample Space
You can use the idea of a tree to determine the size of a sample space without
actually listing it.
How many outcomes are there for:
(a) throwing a 5 sided dice
followed by throwing
a 10 sided dice?
(b) throwing a 6 sided dice
followed by tossing a coin
followed by randomly picking
one of the numbers 1, 2, and 3?
Tables: When there are more than 1 or 2 outcomes, a tree can get messy. A table is
an excellent choice for these situations.
A 4 sided dice then a 6 sided dice are thrown. Show the sample space.
1
2
3
4
1
2
3
4
(a) What is the probability of throwing a sum of 7?
(b) What is the probability of throwing a difference of 1?
(c) What is the probability of throwing an even sum?
3
5
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Applications of Mathematics 12
Sample Space
ASSIGNMENT:
1.
Determine the number of different possible outcomes when each of the following
pairs of dice are rolled at the same time. Use the image of a probability tree.
(a) a 6-sided die and an 8-sided die
(b) a 8-sided die and an 12-sided die
(c) a 10-sided die and an 6-sided die
3.
Create a sample space for each of the following events.
(a) A card is drawn from a deck containing only the red face cards and a coin is
tossed. Use a table.
J♡
Q♡
K♡
J
Q
K
H
T
(b) A number from 1 to 3 is picked and a letter from the word MATH is chosen.
Use a table
M
1
2
3
4
A
T
H
Applications of Mathematics 12
4.
Sample Space
An 8-sided die numbered 0 to 7 and a 4-sided die numbered 1 to 4 are rolled at the same time.
(a) Create a sample space for this experiment, using a table. Write small and include the sum in
each cell, to help answer the questions below:
1
2
3
4
0
1
2
3
4
5
6
7
(b) Determine the probability that the sum
of the two dice will be 10.
(c) Determine the probability that the sum
of the two dice will be an even number.
(d) Which sums have the greatest probability of occurring?
(e) What is the probability that the sum of the
two dice will be less than 10?
Calculate your answer in two different ways.
(f) Which sums have a probability of occurring of
5
3
?
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Applications of Mathematics 12
5.
Construct a tree diagram to show the sample space for a 4-question true/false test.
What is the probability that all 4 questions will be answered correctly by random
guessing?
*** the tree will have 4 levels, each one branching into
6
Sample Space
C correct or W wrong
Work with a partner through the textbook pages 17&18 # 3, 7, 8.
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