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Experiment, Trial and Outcome
Sample Space
Event
Special Events
Events As Sets
Mutually Exclusive Events
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An experiment is an activity with an observable outcome.
Each repetition of the experiment is called a trial. In each
trial we observe the outcome of the experiment.
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Experiment 1: Flip a coin
Trial: One coin flip Outcome: Heads
Experiment 2: Allow a conditioned rat to run a
maze containing three possible paths
Trial: One run
Outcome: Path 1
Experiment 3: Tabulate the amount of rainfall in
New York, NY in a year
Trial: One year
Outcome: 37.23 in.
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The set of all possible outcomes of an experiment
is called the sample space of the experiment. So each
outcome is an element of the sample space.
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An
experiment consists of throwing two dice, one
red and one green, and observing the numbers on
the uppermost face on each. What is the sample
space S of this experiment?
Each outcome of the experiment can be regarded
as an ordered pair of numbers, the first
representing the number on the red die and the
second number on the green die.
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
S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6) (3,1),
(3,2), (3,3), (3,4), (3,5), (3,6) (4,1), (4,2),
(4,3), (4,4), (4,5), (4,6) (5,1), (5,2), (5,3),
(5,4), (5,5), (5,6) (6,1), (6,2), (6,3), (6,4),
(6,5), (6,6)}
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An
event E is a subset of the sample space. We say
that the event occurs when the outcome of the
experiment is an element of E.
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For
the experiment of rolling two dice, describe the
events
E1 = {The sum of the numbers is greater than 9};
E2 = {The sum of the numbers is 7 or 11}.
E1 = {(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)}
E2 = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1), (5,6),

(6,5)}
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Let S be the sample space of an experiment.
The event corresponding to the empty set, , is
called the impossible event, since it can never occur.
The event corresponding to the sample space itself,
S, is called the certain event because the outcome
must be in S.
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Let E and F be two events of the sample space S.
The event where either E or F or both occurs is designated by EF.
The event where both E and F occurs is designated by E F.
The event where E does not occur is designated by E '.
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For the experiment of rolling two dice, let
E1 = “The sum of the numbers is greater than 9”
and
E3 = “The numbers on the two dice are equal”.
Determine the sets
E1 E3, E1  E3, and (E1 E3)'.
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E1 = {(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)}
E3 = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}
E1 E3 = {(1,1), (2,2), (3,3), (4,4), (4,6), (5,5),
(5,6), (6,4), (6,5), (6,6)}
E1  E3 = {(5,5), (6,6)}
(E1 E3)' = {(1,2), (1,3), (1,4), (1,5), (1,6), (2,1),
(2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,4),
(3,5), (3,6), (4,1), (4,2), (4,3), (4,5), (5,1),
(5,2), (5,3), (5,4), (6,1), (6,2), (6,3)}
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Let E and F be events in a sample space S. Then E and F are mutually exclusive
(or disjoint) if
EF =.
If E and F are mutually exclusive, then E and F cannot simultaneously occur; if
E occurs, then F does not; and if F occurs, then E does not.
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For the experiment of rolling two dice, which of
the following events are mutually exclusive?
E1 = “The sum of the dots is greater than 9”
E2 = “The sum of the dots is 7 or 11”
E3 = “The dots on the two dice are equal”
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E1 = {(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)}
E2 = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1), (5,6),
(6,5)}
E3 = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}
E1  E2 = {(5,6), (6,5)} - Not mutually exclusive
E1  E3 = {(5,5), (6,6)} - Not mutually exclusive
E2  E3 =  - Mutually exclusive
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The sample space of an experiment is the set of all
possible outcomes of the experiment. Each subset
of the sample space is called an event. We say that
an event occurs when the outcome is an element of
the event.
 The event E F occurs when either E or F or both
 E F occurs when both E and F
occurs. The event
occur. The event E' occurs 
when E does not occur.

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Two events are mutually exclusive if they cannot
both occur at the same time.

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