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Math 141 Lecture Notes
Section 7.1 Experiments, Sample Spaces, and Events
Terminology
An experiment is an activity with observable results.
The results of the experiment are called the outcomes of the experiment.
An outcome of an experiment is a sample point.
The set consisting of all possible sample points of an experiment is the sample space.
A sample space associated with an experiment that has a finite number of possible
outcomes (sample points) is called a finite sample space.
A subset of a sample space of an experiment is an event.
Example 1: Describe the sample space associated with the experiment of tossing a
coin and observing whether it falls “heads” or “tails.” What are the events of this
experiment?
Venn diagrams can be used to depict the union, intersection, and complementation of
events.
Example 2: Consider the experiment of casting a die and observing the number that
falls uppermost. Let S = {1, 2, 3, 4, 5, 6} denote the sample space of the experiment and
E = {2, 4} and F = {1, 3, 5} be events of this experiment. Compute the following and
interpret your results.
a. E  F
b. E  F
c. F C
E and F are mutually exclusive if E  F = .
Example 3: An experiment consists of tossing a coin three times and observing the
resulting sequence of “heads” and “tails.”
a. Describe the sample space S of the experiment.
b. Determine the event E that at least two heads appear.
c. Determine the event F that at exactly one head appears.
Example 4: An experiment consists of casting a pair of dice and observing the number
that falls uppermost on each die.
a. Describe an appropriate sample space S for this experiment.
b. Determine the events E 2 , E3 , E 4 ,..., E12 that the sum of the numbers falling
uppermost is 2, 3, 4, …, 12, respectively.
Example 5: The manager of a local cinema records the number of patrons attending a
first-run movie at the 1 p.m. screening. The theater has a seating capacity of 500.
a. What is an appropriate sample space for this experiment?
b. Describe the event E that more than 400 people attend the screening.
c. Describe the event F that the theater is less than half full at the screening.
Example 6: An experiment consists of studying the composition of a three-child family
in which the children were born at different times.
a. Describe an appropriate sample space S for this experiment.
b. Describe the event E that there are two boys and a girl in the family.
c. Describe the event F that the oldest child is a boy.
d. Describe the event G that the oldest child is a girl and the youngest child is a boy.
Example 7: EverBrite is developing a high-amperage, high-capacity battery as a source
for powering electric cars. The battery is tested by installing it in a prototype electric car
and running the car with a fully charged battery on a test track at a constant speed of 55
mph until the car runs out of power. The distance covered by the car is then observed.
a. What is the sample space for this experiment?
b. Describe the event E that the driving range under test conditions is less than 140
miles.
c. Describe the event F that the driving range is between 200 and 250 miles
inclusive.
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