Download Section 13.1 Assignment

Section 13.1
The Basics of Probability
Theory
NCSCOS 2.02
Objectives:
 Determine sample space.
 Describe events as a subset.
 Compute Empirical Probability.
 Compute Theoretical Probability.
Key Terms:
 Experiment: any observation of a random
phenomenon.
 Outcomes: the different possible results of the
experiment.
 Sample space: the set of all possible outcomes for an
experiment.
 Event: a subset of the sample space, denoted by E.
Example 1:
 Finding Sample Spaces
 We select an item from a production line and
determine whether it is defective or not.
Example 2:
 Finding Sample Spaces
 Four children are born to a family and we note
the birth order in respect to sex.
Some Good Advice:
 Although we usually describe events verbally, you
should remember that an event is always a subset of
the sample space.You can use the verbal description
to identify the set of outcomes that make up the
event.
Example 3:
 Describe events as subsets.
 A head occurs when we flip a coin.
Example 4:
 Describe events as subsets.
 Three girls and one boy are born to a family.
Key Terms:
 Probability of an Outcome (in a sample space):
a number between 0 and 1 inclusive.
 Probability of an Event: defined as the sum of
the probabilities of the outcomes that make up E,
denoted by P(E).
Key Concept:
 Empirical Probability: if E is an event and we
perform an experiment several times, then we
estimate the probability of E as follows:
 P(E) =
the number of times E occurs
the number of times the experiment is performed
Example 5:
 Using Empirical Information to Assign Probabilities
 A pharmaceutical company is testing a new flu vaccine. The
experiment is to inject a patient with the vaccine and observe
the occurrence of side effects. Assume that we perform the
experiment 100 times and obtain the information in the table.
 Based on the table, if a physician injects a patient with this
vaccine, what is the probability that the patient will develop
mild side effects?
Side
Effects
None
Number of
Times
67
Mild
25
Severe
8
Example 6:
 Using Empirical Probability
 We obtain red exactly once in two spins.
Yellow
Red
Blue
Example 7:
 Using Empirical Probability
 Red appears exactly twice in three spins.
Yellow
Red
Blue
Key Concept:
 Calculating Probability When Outcomes Are Equally Likely:
 If S is a sample space with all equally likely outcomes, then each
outcome has a probability equal to:
1
number of outcomes in S
 For an event E in this sample space,
P(E) = n(E)
n(S)
= 1
n(S)
Example 8:
 Computing Probability of Events
 What is the probability in a family with three children
that two of the children are girls?
Example 9:
 Computing Probability of Events
 If we roll two fair dice, what is the probability of
rolling a total of eight?
1
1
2
3
4
5
6
2
3
4
5
6
Example 10:
 Computing Probability of Events
 If we select two cards randomly from a standard 52-
card deck, what is the probability that both are face
cards?
Section 13.1 Assignment
 Classwork:
 TB pg. 730/1 – 20 All
 Remember you must write problems and show ALL
work to receive credit for this assignment.
Section 13.1 Continued
The Basic of Probability
Basic Properties of Probability
 Assume that S is a sample space for some
experiment and E is an event in S.
1. 0 < P(E) < 1
2. P(ø) = 0
3. P(S) = 1
Example 11:
 Using Probability to Explain Genetic Diseases
 TB pg. 731/25
Example 12:
 TB pg. 731/27
Example 13:
 TB pg. 731/29
Key Concept:
 Probability for Computing Odds.
 If E’ is the complement of the event E, then the
odds against E are:
P(E’)
P(E)
Example 14:
 TB pg. 731/31
Example 15:
 TB pg. 731/33
Example 16:
 TB pg. 732/41
Example 17:
 TB pg. 732/47
1
1
2
3
4
5
6
2
3
4
5
6
Example 18:
 TB pg. 733/51
Section 13.1 Assignment
 Class work:
 TB pg. 730/1 – 20 All…due 11/18
 Remember you must write problems and show ALL
work to receive credit for this assignment.
 TB pg. 731/26 – 52 Even…due 11/18

Remember you must write problems and show ALL
work to receive credit for this assignment.