Download 10/24 Intro to Probability

FST 10/24/16
Basic Principles of Probability_
Name: ______________
Probability Theory is the branch of mathematics that studies chance. To begin this study we define some of
the basic vocabulary.
The Outcomes and Sample Space of an Experiment
is a situation that has several possible results.
The results are called:
.
Experiment
Outcomes
Tossing a coin.
Tossing two coins.
Rolling a die.
Rolling two dice and recording the sum.
Rolling two dice and recording the value of each die.
The set of all possible outcomes of an experiment is the
of the experiment.
An
is any subset of a sample space of an experiment.
Example 1
For the experiment of a family having three children, list the sample space. List the outcomes in the event of
having at least two boys.
The probability of an event measures the likelihood that the event will occur; probabilities are typically
written as a decimal or as a fraction.
≤ P(E) ≤
The probability that an event will occur is:
.
Notation:
N(E) represents the number of elements in a set E and N(S) represents the number of elements in a set S. Let
S be a sample space for rolling a die and let E be the event of rolling an even number.
S = {1, 2, 3, 4, 5, 6}
E={
N(S) =
}
N(E) =
Definition:
Let E be an event in a finite sample space S. If each outcome in S is equally likely, then the probability that E
occurs, denoted P(E), is given by
Examples:
Suppose two fair dice are rolled.
a.
Find N(S).
b.
Find P(sum of dice = 7)
c.
Find the P(sum of dice < 10)
d.
Find the P(sum of dice = 1)
e.
Find the P(sum of dice < 50)
f.
Find the P(doubles)