Download Lesson 5.1 Introduction to Probability Notes

Lesson 5.1 Introduction to Probability Notes
Statistics
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Experimental Probability
 The probability of an event happening is between 0 and 1, inclusive.
 If an event has a 0% chance of happening (the event is impossible), what is the
assigned probability?
 If an event has a 100% chance of happening (the event is certain), what is the
assigned probability?
 If an event has a 50% chance of happening, what is the assigned probability?
 All events have an assigned probability between ______ and ________.
Definitions:
 Event: a collection of one or more outcomes of a statistical experiment or
observation.
 Probability Theory: the study of the chance (or likelihood) of events happening
 Trials: total number of times the experiment is repeated
 Outcomes: different results possible for one trial of the experiment
 Frequency: number of times a particular outcome is observed
 Relative frequency also called experimental probability: frequency expressed as a
fraction or percentage of the total number of trials.
 Sample space: set of all possible outcomes of an experiment
 Law of large numbers: the more trials in the experiment, the closer to theoretical
probability
Notation:
 P(heads) = 0.5
P(tails) = 0.5
 P(A), read “P of A” denotes the probability of event A.
 P(A) = 1, the event A is certain to occur.
 P(A) = 0, the event A is certain not to occur.
Probability Assignments:
 Intuition: incorporates past experiences, judgment, or opinion to estimate the
likelihood of an event
 Relative Frequency: P( A) 
frequency of the event
f

the total number of possible outcomes n
 Theoretical Probability: equally likely outcomes
P( E ) 
the number of members of the event E
the total number of possible outcomes
Lesson 5.1 Introduction to Probability Notes
Statistics
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Example 1: Assign a probability to the indicated event on the basis of the information provided.
Indicate the technique used: intuition, relative frequency, or theoretical probability
a. A random sample of 500 students at ASU were surveyed. It was determined that 375 wore
glasses. Estimate the probability that a student selected at random wore glasses.
b. The Friends of the Library host a fund raising lunch. You are on the clean-up
committee. There are four members on this committee. There is a drawing to
determine who will clean the bathrooms. Assume each member has an equal chance
of being drawn, what is the probability that you have to clean the bathrooms?
c. Sally photographs sea lions for Sea World. During her next session, she is to
photograph sea lions eating fish. Based on her knowledge of sea lions, she believes
she will be successful. What specific number do you suppose she would estimate for
the probability of success?
Sample Space
Example 2: List the sample space of possible outcomes for:
a. tossing a coin
b. rolling a die
c. tossing two coins
d. rolling a die and flipping a coin
Example 3: There are going to be 3 True-False questions on a test.
a. List the sample space.
b. What is the probability that all three will be false?
c. What is the probability that exactly two question will be false?
Lesson 5.1 Introduction to Probability Notes
Statistics
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Theoretical Probability
 Mathematical (or theoretical probability): a measure of the chance of that event
occurring in any trial of the experiment

P( E ) 
the number of members of the event E
the total number of possible outcomes
Example 4: A ticket is randomly selected from a basket containing 3 green, 4 yellow and 5 blue
tickets. Determine the probability of getting:
a. a green ticket
b. a green or yellow ticket
c. an orange ticket
d. a green, yellow, or blue ticket
 The probability that an event will occur, P(E), is always 0  P( E)  1 . It is always
between 0 and 1, inclusive.
 Complementary Events - E ' : a measure that the event will not occur
 If E is an event, the E’ is the complementary event of E, thus P( E)  P( E ')  1 and
P( E not occurring)  1  P( E occurring) .
Example 5: If P(A)= 0.35m then what is the value of P(A C)?
Example 6: An ordinary 6 – sided die is rolled once. Determine the chance of
a. Getting a 6.
b. Not getting a 6
c. Getting a 1 or 2
Lesson 5.1 Introduction to Probability Notes
Statistics
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d. Not getting a 1 or 2
Example 7: What is the probability that a randomly chosen person has his/her next birthday
on:
a. a Tuesday
b. a week – end
c. in July
d. in January or February
Probability related to Statistics
 Probability is the field of study that makes statements about what will occur when
samples are drawn from a known population.
 Statistics is the field of study that describes how samples are to be obtained and how
inferences are to be made about unknown populations.
Example 8: Determine whether each of the following examples is a probability application
or a statistical application.
a. Randomly select two students from a class which has 14 boys and 18 girls. What is
the probability that both selected students are boys?
b. Randomly interview 100 high school students and ask them how much time they
spent on sports each week and find their average. Based on the sample results, make
a conjecture about the average amount of time a high school student would spend on
sports per week.
Assignment: p. 164 #2, 3, 4, 6cd, 9, 12, 13