Chapter 6
Lesson 6.1
Probability
6.1: Chance Experiments and Events
Suppose two six-sided die is rolled and
they both land on sixes.
Or a coin is flipped and it lands on heads.
Or record the color of the next 20 cars to
pass an intersection.
These would be examples of chance experiments.
Chance experiment – any activity or
situation in which there is uncertainty
about which of two or more plausible
outcomes will result.
Suppose a six-sided die is rolled. The
possible outcomes are that the die could
land with 1 dot up or 2, 3, 4, 5, or 6 dots
up.
S = {1, 2, 3, 4, 5, 6}
The sum of the
“S”
stands
for
sample
space.
We
use
set notation
to list
This would be an example of probabilities
a sample
space.
of the
the outcomes of the sample space.
outcomes in the sample
space equals ____.
Sample space - the collection of all
possible outcomes of a chance
experiment
Suppose two coins are flipped. The sample
space would be:
S = {HH, HT, TH, TT}
Where H = heads and T = tails
We can also use a Tree Diagram to represent a sample
space.
H
H
T
T
H
T
We
HTfollow the
branches out to
show an
outcome.
Suppose a six-sided die is rolled. The
outcome that the die would land on an even
number would be
E = {2, 4, 6}
This would be an example of an event.
We typically use capital letters to denote an event.
Event - any collection of outcomes
(subset) from the sample space of a
chance experiment
Suppose a six-sided die is rolled. The
event that the die would land on an even
number would be
E = {2, 4, 6}
The sum of the
probabilities of
The
superscript
“C”
What
would
the
be
that
is
the
die
E’event
and E also
denote
complementary
stands for complement
of E events equals
NOT landing onthe
ancomplement
even number?
______.
EC = {1, 3, 5}
This is an example of complementary events.
Complement - Consists of all outcomes
that are not in the event
These complementary events can be shown
on a Venn Diagram.
E = {2, 4, 6} and EC = {1, 3, 5}
Let the circle represent event
E.
Let the rectangle represent
the sample space.
Let the shaded area represent
event not E.
Suppose a six-sided die is rolled. The event
that the die would land on an even number
would be E = {2, 4, 6}
The event that the die would land on a prime
number would be P = {2, 3, 5}
What would be the event E or P happening?
E or P = {2, 3, 4, 5, 6}
This is an example of the union of
two events.
The union of A or B - consists of all
outcomes that are in at least one of the
two events, that is, in A or in B or in both.
A or B  A  B
Consider a
The is
bride
marriage
or to the
This
similar
takes
allof
her
union
of
two
union
A and B.
stuff –& when
the
people
All of A and all of B
groom
takes
two
people
are put together!
all
his stuff
marry,
what&
they
pooldo
it
do they
together!
with
their
possessions ?
This symbol means
And live happily
“union”
ever
after!
Let’s revisit rolling a die and getting an even
or a prime number . . .
E or P = {2, 3, 4, 5, 6}
E or way
P would
be any this is with a Venn Diagram.
Another
to represent
number in either circle.
Even number
Why is the number 1
outside the circles?
6
1
Prime number
4
3
2
5
Suppose a six-sided die is rolled. The event that
the die would land on an even number would be
E = {2, 4, 6}
The event that the die would land on a prime
number would be P = {2, 3, 5}
What would be the event E and P happening?
E and P = {2}
This is an example of the
intersection of two events.
The intersection of A and B - consists of
all outcomes that are in both of the events
A and B  A  B
This symbol means
“intersection”
Let’s revisit rolling a die and getting an even
or a prime number . . .
E andbeP ONLY
= {2}
E and P would
the middle
To represent
thispart
withthat
a Venn Diagram:
the circles have in
common
4
6
1
3
2
5
Suppose a six-sided die is rolled.
Consider the following 2 events:
A = {2}
B = {6}
On a single die roll, is it possible for A
and B to happen at the same time?
These events are mutually exclusive.
Mutually exclusive (or disjoint) events two events have no outcomes in common;
two events that NEVER happen
simultaneously
A Venn Diagram for the roll of a six-sided
die and the following two events:
A = {2} B = {6}
A and B are mutually
The intersection of A and
exclusive (disjoint) B is empty!
since they have no
outcomes in common
4
6
2
1
5
3
Practice with Venn Diagrams
On the following four slides you will find
Venn Diagrams representing the students
at your school.
Some students are enrolled in Statistics,
some in Calculus, and some in Band.
For the next four slides, indicate what
relationships the shaded regions represent.
Statistics
Calculus
Band
Calculus or Band
Statistics
Calculus
Band
Statistics or Band and not Calculus
Statistics
Calculus
Band
Com
Sci
Statistics and Band and not Calculus
Statistics
Calculus
Band
Statistics and not (Band or Calculus)
M&M Activity
Homework
• Pg.326: #6.3, 6.5, 6.8, 6.9, 6.11, 6.12
• Reading Notes 6.2