Download 3.1 Basic Concepts of Probability

Statistics
3.1 Basic Concepts of Probability
Objectives: Probability Experiments; Types of Probability; Complementary Events
Procedure:
1. Probability Experiments:
a. Definition 1: A ______________________________________ is an
action, or trial, through which specific results (counts, measurements, or
responses) are obtained. The result of a single trial in a probability
experiment is an ____________. The set of all possible outcomes of a
probability experiment is the ___________________. An _____________
consists of one or more outcomes and is a subset of the sample space.
b. Examples 1 & 2: Identifying the sample space of a probability experiment:
1. A probability experiment consists of a coin and then rolling a six-sided
die. Describe the sample space.
2. A probability experiment consists of recording a response to the
survey statement below and the gender of the respondent.
Survey
There should be a limit
to the number of terms
a U.S. senator can serve.



Agree
Disagree
No Opinion
c. Definition 2: An event that consists of a single outcome is called a
_______________________.
d. Example 3: Identifying simple events:
Decide whether each event is simple or not. Explain your reasoning.
1. For quality control, you randomly select a computer chip from a
batch that has been manufactured that day. Event A is selecting
a specific defective chip.
2. You roll a six-sided die. Event B is rolling at least a 4.
2. Types of Probability:
a. Definition 3: __________________ (or _____________) _____________
is used when each outcome in a sample space is equally likely to occur.
The classical probability for an event E is given by
b. Examples 4 & 5: Finding classical probabilities:
4. You roll a six-sided die. Find the probability of each event.
1. Event A: rolling a 3
2. Event B: rolling a 7
3. Event C: rolling a number less than 5.
5. You select a card from a standard deck of cards. Find the probability of
each event.
1. Event A: Selecting a seven of diamonds
2. Event B: Selecting a diamond
3. Event C: Selecting a diamond, heart, club, or spade.
c. Definition 4: _______________ (or ______________) ______________
is based on observations obtained from probability experiments. The
empirical probability of an event E is the relative frequency of event E.
d. Example 6: Finding empirical probabilities:
A pond contains three types of fish: bluegills, red gills, and crappies. Each
fish in the pond is equally likely to be caught. You catch 120 fish and
record the type. Each time, you release the fish back into the pond. The
frequency distribution shows your results. If you catch another fish, what is
the probability that it will be a bluegill?
Fish Type
Bluegill
Red gill
Crappy
Number of times caught, f
39
51
30
 f  120
e. Definition 5: ______________________________: As an experiment is
repeated over and over, the empirical probability of an event approaches
the theoretical (actual) probability of the event.
f. Example 7: Using frequency distributions to find probabilities:
You survey a sample of 100 employees at a company and record the age
of each. The results are shown below in the frequency distribution. If you
randomly select another employee, what is the probability that the
employee will be between 25 and 34 years old?
Employee ages
15 to 24
25 to 34
35 to 44
45 to 54
55 to 64
65 and over
Frequency, f
54
366
233
180
125
42
 f  1000
g. Definition 6: _______________________________ result from intuition,
educated guesses, and estimates.
h. Example 8: Classifying types of probability:
Classify each statement as an example of classical probability, empirical
probability, or subjective probability. Explain your reasoning.
i. The probability that you will be married by the age of 30 is 0.5.
ii. The probability that a voter chosen at random will vote Republican
is 0.45.
iii. The probability of winning a 1000-ticket raffle with one ticket is
1
.
1000
i.
Definition 7: ______________________: The probability of an event E is
between 0 and 1, inclusive. That is,
3. Complementary Events:
a. Definition 8: The _________________________ is the set of all
outcomes in a sample space that are not included in event E. The
complement of event E is denoted by E’ and is read as “E prime.”
b. Example 9: Finding the probability of the complement of an event:
Use the frequency distribution in the employee ages example to find the
probability of randomly choosing an employee who is not between 25 and
34 years old.
4. HW: p. 125 (1 – 3 all, 7 – 12 all, 15 – 39 mo3)