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Mr. Wolf
Thursday 1/22/09
Pre-Calculus
Grades 10-12
Unit 7: Probability & Statistics
Probability
Materials and Resources:
 Warm-up (1 per student)
 Probability Notes Sheet (1 per student)
 Probability Practice Problems (1 per student)
 Exit Ticket (1 per student)
PA Standards Addressed:
Instructional Objectives:
 Students will be able to determine the probability and odds of a simple event.
 Students will be able to determine the probability of two events occurring
simultaneously or separately.
 Students will be able to discern between independent, mutually exclusive, and
complementary events.
Time
10 min
1 min
5 min
Activity
Warm-up
Agenda
Homework Check
min
Review Homework
min
1 min
5 min
Agenda
Conclusion
Homework:
Pg. 709-711 #11-20, 33, 38
Review Packet #19-27
Lesson Reflection:
Description
Pass out the Warm-up and review solutions.
Review the goals for the day.
Spot-check and instruct students to copy their
solution to pg. # onto the back of the Warm-up.
Collect and grade.
Present the HW solutions and answer any
questions.
Modeling:
Guiding:
Independent Practice:
Assessment:
Modifications:
Students with special needs…
Advanced students…
Revisit goals and identify whether they were met.
Pass out the Exit Ticket and collect at the bell.
Pre-Calculus /Trigonometry 3
Fall 2008
Name: ____________________________
Date: ____________
Block: ______
Warm-up
Counting Principles
Jack is interested in dating five different girls at his school. In a weekend, Jack can go
out with three different girls at three different times (Friday night, Saturday night, Sunday
afternoon).
1) In one weekend, how many ways can Jack see a different girl at each time
possible? (Does order matter?)
2) What is the likelihood that Jack goes out with Mary (one of the five girls) on
Friday night?
3) What is the likelihood that Jack goes out with Mary sometime during the
weekend?
4) What is the likelihood that the girls find out that Jack is trying to date five
different girls and none of them speak to him again?
Pre-Calculus/Trigonometry 3
Name: ____________________________
Date: ____________
Block: ______
Warm-up
Counting Principles
Jack is interested in dating five different girls at his school. In a weekend, Jack can go
out with three different girls at three different times (Friday night, Saturday night, Sunday
afternoon).
1) In one weekend, how many ways can Jack see a different girl at each time
possible? (Does order matter?)
2) What is the likelihood that Jack goes out with Mary (one of the five girls) on
Friday night?
3) What is the likelihood that Jack goes out with Mary sometime during the
weekend?
4) What is the likelihood that the girls find out that Jack is trying to date five
different girls and none of them speak to him again?
Pre-Calculus /Trigonometry 3
Fall 2008
Name: ____________________________
Date: ____________
Block: ______
Probability
Notes Sheet
Any happening for which the result is uncertain is called an experiment. The possible
results of the experiment are outcomes, the set of all possible outcomes of the experiment
is the sample space, and any subcollection of a sample space is an event.
Example
Experiment: rolling a six-sided die
Sample Space: {1, 2, 3, 4, 5, 6}
Event: rolling a 4
outcomes
The Probability of an Event
To calculate the probability of an event E, count the number of outcomes of the event n(E) and the number
of outcomes in the sample space n(S) and use the following formula:
P( E ) 
n( E ) # winners

n( S )
total
Examples:
1) Two coins are tossed. What is the probability that both land heads up?
2) A six-sided die is rolled. Calculate the following probabilities:
a. P(rolling a 5) =
b. P(rolling an even number) =
c. P(rolling an odd number) =
d. P(rolling a prime number) =
3) A card is chosen from a 52-card deck. Calculate the following probabilities:
a. P(choosing a King) =
b. P(choosing a diamond) =
c. P(choosing a face card) =
d. P(choosing a face card and a diamond) =
Pre-Calculus /Trigonometry 3
Fall 2008
Name: ____________________________
Date: ____________
Block: ______
Probability of Two Events Occurring
The probability of event A and event B both occurring is written:
P ( AB) or P ( A  B ) or “A intersect B”
The probability of two events both occurring is given by: P( AB) 
The probability of event A or event B occurring is written:
P(A or B) or P ( A  B ) or “A union B”
The probability of event A or event B occurring is given by:
P(A or B) = P( A)  P( B)  P( AB)
# winners
total
Venn Diagrams can be
helpful when calculating
the probability of two
events occurring.
Example:
One card is selected from a standard deck of 52 playing cards.
a. What is the probability that the card is both a heart and a face card?
b. What is the probability that the card is either a heart or a face card?
Types of Events
Two events A and B are called mutually exclusive if A and B have no outcomes in common so P( AB)  0 .
Two events are called independent if the occurrence of one has no effect on the occurrence of the other. If A
and B are independent events, the probability that both A and B will occur is given by: P( AB)  P( A) • P(B) .
The complement of an event A is the collection of all outcomes in the sample space that are not in A and is
written A’. The probability of the complement of event A is given by: P( A' )  1  P( A) .
Examples:
1) Event A = Phillies winning the World Series
Event B = Mets winning the World Series
What type of events are these? Why?
2) A student rolls a 6-sided die and tosses a coin. What is the probability he rolls an even
number and the coin lands on heads?
3) There are four red marbles, six black marbles, and eight blue marbles in a jar. What is
the probability of not picking a red marble?
Pre-Calculus /Trigonometry 3
Fall 2008
Name: ____________________________
Date: ____________
Block: ______
Probability
Practice Problems
1) Find the probability for the experiment of tossing a coin three times. Use the
sample space S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
a. P(exactly one tail) =
b. P(getting a tail on the first toss) =
c. P(at least one head) =
d. P(at least two heads) =
2) Find the probability for the experiment of drawing two marbles from a bag
containing one green, two yellow, and three red marbles.
a. P(both are red) =
b. P(both are yellow) =
c. P(neither is yellow) =
d. P(marbles are different colors) =
3) One hundred college students were interviewed to determine their political party
affiliations and whether they favored a balanced-budget amendment to the
Constitution. The results of the study are listed in the table, where D represents
Democrats and R represents Republicans. A person is randomly selected from the
sample. Find the probability that the described person is selected.
a. A person who does not favor the amendment.
b. A Republican.
c. A Democrat who favors the amendment.
D
R
Total
Favor
23
32
55
Not Favor
25
9
34
Unsure
7
4
11
Total
55
45
100
Pre-Calculus /Trigonometry 3
Name: ____________________________
Fall 2008
Date: ____________
Block: ______
4) A class is given a list of 20 study problems, from which 10 will be selected for an
upcoming exam. A student knows how to solve 15 of the problems. Find the
probability that the student will be able to answer…
a. all 10 questions on the exam
b. exactly eight questions on the exam
c. at least nine questions on the exam
5) The figure shows the results of a recent survey in which 1011 adults were asked
to grade U.S. public schools.
a. Estimate the number of adults who gave public schools a B.
b. An adult is selected at random. What is the probability that the adult will give the
U.S. public schools an A?
c. An adult is selected at random. What is the probability that the adult will give the
U.S. public schools a C or D?
Pre-Calculus /Trigonometry 3
Fall 2008
Name: ____________________________
Date: ____________
Block: ______
Exit Ticket
Probability
You have two dice, two coins, and a deck of playing cards (52 cards total). Determine
the probabilities of the following events.
Event A = flipping two heads
Event B = rolling a sum of 10
Event C = choosing a King
1) P(A) =
2) P(B) =
3) P(C) =
4) P(AB) =
5) P(BC) =
Pre-Calculus/Trigonometry 3
Fall 2008
Name: ____________________________
Date: ____________
Block: ______
Exit Ticket
Probability
You have two dice, two coins, and a deck of playing cards (52 cards total). Determine
the probabilities of the following events.
Event A = flipping two heads
Event B = rolling a sum of 10
Event C = choosing a King
1) P(A) =
2) P(B) =
3) P(C) =
4) P(AB) =
5) P(BC) =