1. 7.2 Definition of Probability
Unit 7 - Probability
7.2 Definition of Probability

2. Simple Events
Let S be a finite sample space with n outcomes; S = {s1, s2, s3, …, sn}. The simple events are those that consist of exactly one point of the experiment: {s1}, {s2}, {s3}, …, {sn}.

3. Ex: An opinion poll is conducted among a group of registered voters
Ex: An opinion poll is conducted among a group of registered voters. Their political party (D, R, I) and gender (m, f) are recorded. List the simple events of this experiment.
The simple events of an experiment are mutually exclusive; meaning, only one can occur at a time.

4. Probability
The probability of an event occurring is a measure of the proportion of the time that the event will occur in the long run.
Suppose that in n trials an event E occurs m times. The relative frequency of the event E is m/n.
If the relative frequency approaches some value P(E) as n becomes larger, then P(E) is called the empirical probability of E.

5. Coin-Tossing Experiment
Flip a coin n times and record the number of heads.
Number tosses (n)
Number heads (m)
Relative Frequency of Heads (m/n) 10 4
.4000
100 58
.5800
1,000
492
.4920
10,000
5,034
.5034
20,000
10,024
.5012
40,000
20,032
.5008

6. A probability distribution is a table that lists the probability of each simple event of an experiment.
Ex. The table below represents the frequency of certain types of license plates observed by a family on a recent trip. Find the probability distribution.
State
Number
Wisconsin 45
Illinois 80
Iowa 20
Indiana 5

7. Properties of Probability Distributions
The probability of each simple event is between 0 and 1 inclusive.
2. The sum of the probabilities of all events in a sample space is 1.
3. The probability of the union of two mutually exclusive events is given by the sum of their probabilities.