Download Math 241 Notes 5.1

Section 5.1 Probability Rules
Objectives: Compute probabilities using empirical and classical methods.
Probability is the likelihood of a random phenomenon or chance behavior
occurring.
 Values are between 0 and 1, inclusive.
 Can be expressed as fractions, decimals, or percents.
 Probability of event E is denoted by P(E).
 Events with probability close to one are more likely to occur.
 If an event has a probability equal to zero it is an impossible event.
 If an event has probability equal to one, the event is certain to occur.
 An unusual event is an event that has a low probability of occurring
(usually probability less than 5%).
 Used in inferential statistics (using information from a sample to draw
conclusions regarding the population).
1. Are the following numbers valid probabilities?
a.
-0.14
b. 2.17
c. 110%
d.
7
23
A probability experiment is any process with uncertain results that can be
repeated.
The sample space, S, of a probability experiment is the collection of all possible
outcomes.
An event is any collection of outcomes from a probability experiment.
2.
A probability experiment consists of rolling a single fair die.
a. Determine the sample space.
b. Compute the probability of the event E = “roll a number less than
four”
5.1 - 2
The Law of Large Numbers
In the long run, as sample size increases, the relative frequencies of outcomes
gets closer and closer to the theoretical (or actual) probability value.
Three methods for determining the probability of an event:
1.
the empirical method (relative frequency)
2.
the classical method (theoretical probability)
3.
the subjective method
The Empirical Method
P ( E )  relative frequency 
frequency of E
# of trials
As we increase the number of trials, our estimate becomes more accurate (Law
of Large Numbers).
The Classical Method
Theoretical: When outcomes are equally likely — no one result is expected to
occur more frequently than any other. Does not require a probability
experiment be performed.
P( E ) 
# of ways that E can occur
# of possible outcomes
The Subjective Method
A subjective probability of an outcome is a probability obtained on the basis of
personal judgment (intuition).
 Example: A sportscaster announces that an athlete has a 90% chance of
breaking a world record. He is using the past performance of the athlete
and his experience in the field to obtain this probability of 90%. It is a
“feeling”.
Work #1 - 4