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♥ INTERNET EXPLORER 6.0 and above, with MathPlayer installed.♥
BASIC PROBABILITY CONCEPTS
Jump right to the exercises!
PROBABILITY is the area of mathematics devoted to predicting the likelihood of uncertain occurrences.
For example, when you roll a die, it is uncertain whether you'll see the number 1, 2, 3, 4, 5, or 6.
However, it is possible to talk about how likely it is for each number to occur.
A probability is a number between 0 and 1 that represents the likelihood of
occurrence of something.
An experiment is the act of making an observation or taking a measurement.
An outcome is one of the possible things that can occur as a result of an experiment.
The set of all possible outcomes for an experiment is called its sample space, and
is frequently denoted by S .
Any subset of the sample space is called an event, and is frequently denoted by E .
The probability of an event E is denoted by
P(E) .
Given any set A , the notation n(A) is used to denote the number of elements (members)
in A .
EQUALLY LIKELY OUTCOMES:
If every outcome in a sample space S is equally likely to occur,
then the probability of an event E is found by taking the number of outcomes in
E
and dividing by the number of outcomes in S . That is,
P(E)
=
n(E)
n(S)
.
EXAMPLE (single roll of a fair die)
Consider a single roll of a fair die.
The sample space is
S={1
,2,3,4
,5,6}
.
Let x denote the number that is rolled.
The probability of getting a 1 is
16
.
Write this as:
P(x=1
)=1
6 .
Read it aloud as: "The probability that
x is 1 is
1
6 ."
P(x=2
)=1
6
P(x=1
or x=2
)=2
6
Notice that here the event is
E={1
,2} ;
n(E)=
2 ,
n(S)=
6 , and
P(E)=
n(E)
n(S)
=26
=13
.
P(x
is even)=
36
=
12
P(x>1
)=5
6
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.