MATH 166 Spring 2016
1.3
c
Wen
Liu
1.3 Sample Spaces and Events
Definition:
• An experiment is an activity that has observable results.
• An outcome is the result of the experiment.
• A sample space of an experiment is the set of all possible outcomes of the experiment.
• Each repetition of an experiment is called a trial.
Examples:
1. An opinion poll is conducted among a state’s electorate to determine the relationship between
their income levels and their stands on a proposition aimed at reducing state income taxes.
Voters are classified as belonging to either the low-, middle-, or upper-income group. They
are asked whether they favor, oppose, or are undecided about the proposition. Let the letters
L, M, and U represent the low-, middle-, and upper-income groups, respectively, and let the
letters f, o, and u represent their responsesâfavor, oppose, and undecided, respectively.
(a) Describe a sample space S corresponding to this poll.
(b) Describe the event E1 that a respondent favors the proposition.
(c) Describe the event E3 that a respondent does not favor the proposition and does not
belong to the upper-income group.
2. The numbers 5, 6, 7, and 9 are written on separate pieces of paper and put into a hat. Two
pieces of paper are drawn at the same time and the product of the numbers is recorded. Find
the sample space.
Page 1 of 3
MATH 166 Spring 2016
1.3
c
Wen
Liu
Definition:
• Given a sample space S for an experiment, an event is any subset E of S. An elementary (or
simple) event is an event with a single outcome.
Examples:
1. Let S = {5, 6, 15} be a sample space associated with an experiment.
(a) How many total events are there for this sample space?
(b) List all events of this experiment.
(c) How many subsets of S contain the number 6 or the number 15?
2. Two fair 5-sided dice are rolled and the numbers shown uppermost are observed. Find the
number of outcomes in the following events.
(a) The sum of the numbers is 6.
(b) A 4 is rolled.
Page 2 of 3
MATH 166 Spring 2016
1.3
c
Wen
Liu
(c) A 2 is rolled or the sum of the dice is no more than 5.
3. A jar contains 4 marbles numbered 1 through 4. An experiment consists of randomly selecting
a marble from the jar, observing the number drawn, and then randomly selecting a card from
a standard deck and observing the suit of the card (hearts, diamonds, clubs, or spades).
(a) How many outcomes are in the sample space for this experiment?
(b) How many outcomes are in the event “an even number is drawn?”
(c) How many outcomes are in the event “a number more than 3 is drawn and a red card is
drawn?”
(d) How many outcomes are in the event “a number less than 4 is drawn or a club is not
drawn?”
Page 3 of 3