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Computing Probabilities
Sample Spaces and Events
Event
refers to a subset of the
sample space
Sample spaces and events are
sets and they should be written
using “braces”; thus, they are
written in roster form.
EXAMPLE
Three books are to be selected from five
books on a shelf. The books consist of
algebra, geometry, statistics, history, and
physics books. What is the sample space?
What is the event for mathematics books?
EXAMPLE
Two fair dice are rolled and the outcome is
recorded. Write a set for the following
events: (a) sum of 5 and (b) doubles.
Simple Probability
The probability of an event is a numerical
value that describes the likelihood that an
event will happen or not.
It is simply calculated using the ratio of the
cardinality of the event and the cardinality
of the sample space.
EXAMPLE
If you flip two coins, the event “both
heads” is given by the set {HH} and the
sample space is the set {HH, HT, TH, TT}.
What is the probability that the two coins
will land on both heads?
EXAMPLE
A pair of dice is thrown. The event “prime
sum” is the set {(1, 1), (1, 2), (1, 4), (1, 6),
3), (5, 2), (5, 6), (6, 1), (6, 5)}. You know
that there are 36 elements in the sample
space. What is the probability of getting a
sum that is prime?
EXAMPLE
Moira collects stamps from different
countries. She has 10 different stamps
from China, 5 from Thailand, 3 from
France, 6 from USA, and 1 from Venezuela.
Her sister Lindsay borrows one stamp for a
school assignment. What is the probability
that the stamp Lindsay borrows is from
Thailand?
EXAMPLE
Jess has a bag with 6 red, 4 blue, and 8
green marbles. What is the probability that
a marble chosen at random is not red?
EXAMPLE
Marie has 8 books including books on
geometry, chemistry, biology, history,
english, algebra, statistics, and filipino.
What is the probability that her math
books (geometry, algebra, and statistics)
are located at the rightmost part of the
shelf but not necessarily in that order?
Probability Involving a
Sequence of Events
