Week 1: Descriptive Statistics and Probabilities 7
It will be helpful, before we get too much further, to deﬁne some nomenclature and
properties of probabilities and experiments.
Deﬁnition: The sample space S of an experiment is the set containing all possible
outcomes for an experiment.
Example 8: What is the sample space for when a coin is tossed three times?
S =. HHH, TTT, HHT, HTH,
THH, HTT, THT, TTH
Example 9: Two gas stations are located at an intersection. Each one has four gas
pumps. What is the sample space for the experiment in which we measure the number
of pumps in each at each station at a particular time of day.
Deﬁnition: An event is any subset of some predeﬁned sample space S.,n hi
event E is a set of possible outcomes for an experiment.
An event is simple if it contains only one outcome. It is compound if it contains more
than one outcome.
Example 10: Suppose a coin is tossed three times. What is contained in E, the event
that more than two heads come up?
MTHE 224 Fall 2012 Week 1: Descriptive Statistics and Probabilities 8
Example 11: Suppose we re-examine the gas pump example. The sample space is listed
below Determine the set which represents the following events
A \ B 0 1 2 3 4
0 (0,0) (0,1) (0,2) (0,3) (0,4)
1 (1,0) (1,1) (1,2) (1,3) (1,4)
2 (2,0) (2,1) (2,2) (2,3) (2,4)
3 (3,0) (3,1) (3,2) (3,3) (3,4)
4 (4,0) (4,1) (4,2) (4,3) (4,4)
1. Event A, the same number of gas pumps is in use at the same time.
2. Event B, the total number of pumps in use is an even number.