Transcript Presentation

10-9 Probability of Compound Events
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
10-9 Probability of Compound Events
Math Journal (5 Min)
• 3-2-1 - Each student will be given the title of the lesson that will be
taught that day. They must then, at the beginning of class, write 3
statements that they already know about the lesson being
presented, 2 questions that they have before the lesson is
presented, and 1 connection that they feel can be made between
what they already know and what they think they will be taught in
the new lesson before they have been taught the lesson, and at the
end of class, write 3 statements that they now know about the
lesson being presented, answer the 2 questions that they had
written previously, and 1 connection that they now know can be
made between what they knew before the lesson and what they
now know after they have been taught the lesson. Then, each
student will discuss his/her answers within their group. Finally, to
leave class, each student will have to give/write 1 statement or
connection that pertained to the lesson.
10-9 Probability of Compound Events
Homework Review (5 Min)
10-9 Probability of Compound Events
Warm Up
1. Five friends form a basketball team. How many
different ways could they fill the 5 positions on the
team?
5!, or 120
2. The music teacher chooses 2 of her 5 students to
sing a duet. How many combinations for the duet
are possible?
10
10-9 Probability of Compound Events
Problem of the Day
One blue sock and 7 black socks are
placed in a drawer, then picked randomly
one at a time without replacement. What
is the probability that the blue sock is
picked last?
1
8
10-9 Probability of Compound Events
Textbook Examples (I Do) (5 Min)
10-9 Probability of Compound Events
Learn to find probabilities of compound
events.
10-9 Probability of Compound Events
Additional Example 1: Using an Organized List to
Find Probability
A pizza parlor offers seven different pizza
toppings: pineapple, mushrooms, Canadian
bacon, onions, pepperoni, beef, and sausage.
What is the probability that a random order for a
two-topping pizza includes pepperoni?
Let p = pineapple, m = mushrooms, c = Canadian
bacon, o = onions, pe = pepperoni, b = beef, and s =
sausage. Because the order of the toppings does not
matter, you can eliminate repeated pairs.
10-9 Probability of Compound Events
Continued: Check It Out: Example 1
Pineapple – m
Pineapple – c
Pineapple – o
Pineapple – pe
Pineapple – b
Pineapple – s
Mushroom – p
Mushroom – c
Mushroom – o
Mushroom – pe
Mushroom – b
Mushroom – s
Canadian bacon – p
Canadian bacon – m
Canadian bacon – o
Canadian bacon – pe
Canadian bacon – b
Canadian bacon – s
Onions – p
Onions – m
Onions – c
Onions – pe
Onions – b
Onions – s
Pepperoni –p
Pepperoni – m
Pepperoni – c
Pepperoni – o
Pepperoni – b
Pepperoni – s
Beef – p
Beef – m
Beef – c
Beef – o
Beef – pe
Beef – s
P (pe) =
6
=
2
Sausage – p
Sausage – m
Sausage – c
Sausage – o
Sausage – b
Sausage – pe
21
7
The probability that a random two-topping order will include
pepperoni is 2 .
7
10-9 Probability of Compound Events
Check It Out: Example 1
A pizza parlor offers seven different pizza
toppings: pineapple, mushrooms, Canadian
bacon, onions, pepperoni, beef, and sausage.
What is the probability that a random order for
a two-topping pizza includes onion and
sausage?
Let p = pineapple, m = mushrooms, c = Canadian
bacon, o = onions, pe = pepperoni, b = beef, and
s = sausage. Because the order of the toppings
does not matter, you can eliminate repeated pairs.
10-9 Probability of Compound Events
Continued: Check It Out: Example 1
Pineapple – m
Pineapple – c
Pineapple – o
Pineapple – pe
Pineapple – b
Pineapple – s
Mushroom – p
Mushroom – c
Mushroom – o
Mushroom – pe
Mushroom – b
Mushroom – s
Canadian bacon – p
Canadian bacon – m
Canadian bacon – o
Canadian bacon – pe
Canadian bacon – b
Canadian bacon – s
Onions – p
Onions – m
Onions – c
Onions – pe
Onions – b
Onions – s
Pepperoni –p
Pepperoni – m
Pepperoni – c
Pepperoni – o
Pepperoni – b
Pepperoni – s
Beef – p
Beef – m
Beef – c
Beef – o
Beef – pe
Beef – s
P (o & s) =
1
Sausage – p
Sausage – m
Sausage – c
Sausage – o
Sausage – b
Sausage – pe
21
The probability that a random two-topping order will include
onions and sausage is 1 .
21
10-9 Probability of Compound Events
Additional Example 2: Using a Tree Diagram to Find
Probability
Jack, Kate, and Linda line up in random order in
the cafeteria. What is the probability that Kate
randomly lines up between Jack and Linda?
Make a tree diagram showing possible line-up
orders.
Let J = Jack, K = Kate, and L = Linda.
J
K  L = JKL
L  K = JLK
List permutations beginning with Jack.
K
J  L = KJL
L  J = KLJ
List permutations beginning with Kate.
L
J  K = LJK
K  J = LKJ
List permutations beginning with Linda.
10-9 Probability of Compound Events
Additional Example 2: Continued
P (Kate is in the middle)
Kate lines up in the middle
2
1
=
=
=
total number of equally likely line-ups
6
3
The probability that Kate lines up between Jack and
Linda is 1 .
3
10-9 Probability of Compound Events
Check It Out : Example 2
Jack, Kate, and Linda line up in random order in
the cafeteria. What is the probability that Kate
randomly lines up last?
Make a tree diagram showing possible line-up
orders.
Let J = Jack, K = Kate, and L = Linda.
J
K  L = JKL
L  K = JLK
List permutations beginning with Jack.
K
J  L = KJL
L  J = KLJ
List permutations beginning with Kate.
L
J  K = LJK
K  J = LKJ
List permutations beginning with Linda.
10-9 Probability of Compound Events
Check It Out : Example 2 (Continued)
P (Kate is last) =
2
1
Kate lines up last
=
=
total number of equally likely line-ups
6
3
The probability that Kate lines up last is
1
3
.
10-9 Probability of Compound Events
Additional Example 3: Finding the Probability of
Compound Events
Mika rolls 2 number cubes. What is the
probability that the sum of the two numbers will
be less than 4?
There are 3 out of 36 possible outcomes that have a sum less
than 4.
1
The probability of rolling a sum less than 4 is
.
12
10-9 Probability of Compound Events
Check It Out: Example 3
Mika rolls 2 number cubes. What is the
probability that the sum of the two numbers will
be less than or equal to 4?
There are 6 out of 36 possible outcomes that have a sum less
than or equal to 4.
1
The probability of rolling a sum less than or equal to 4 is
.
6
10-9 Probability of Compound Events
Class work Problems (We Do) (10 Min)
• Pg. 448-449 (1-5)
10-9 Probability of Compound Events
10-9 Probability of Compound Events
10-9 Probability of Compound Events
Small Group CW(Yall Do) (10 Min)
• Pg. 448-449 (6-16 EOE)
10-9 Probability of Compound Events
10-9 Probability of Compound Events
10-9 Probability of Compound Events
10-9 Probability of Compound Events
10-9 Probability of Compound Events
10-9 Probability of Compound Events
10-9 Probability of Compound Events
10-9 Probability of Compound Events
10-9 Probability of Compound Events
10-9 Probability of Compound Events
Homework (You Do) (10 Min)
• Pg. 448-449 (7, 9, 11, 13, 15 odd)
10-9 Probability of Compound Events
Math Journal (5 Min)
• 3-2-1 - Each student will be given the title of the lesson that will be
taught that day. They must then, at the beginning of class, write 3
statements that they already know about the lesson being
presented, 2 questions that they have before the lesson is
presented, and 1 connection that they feel can be made between
what they already know and what they think they will be taught in
the new lesson before they have been taught the lesson, and at the
end of class, write 3 statements that they now know about the
lesson being presented, answer the 2 questions that they had
written previously, and 1 connection that they now know can be
made between what they knew before the lesson and what they
now know after they have been taught the lesson. Then, each
student will discuss his/her answers within their group. Finally, to
leave class, each student will have to give/write 1 statement or
connection that pertained to the lesson.
10-9 Probability of Compound Events
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
10-9 Probability of Compound Events
Lesson Quiz
1. The teacher randomly chooses two school days
each week to give quizzes. What is the
probability that he or she chooses Monday and
Wednesday? 1
10
2. A bag contains three red checkers and three
black checkers. Two checkers are randomly
pulled out. What is the probability that 1 red
checker and 1 black checker are chosen? 3
5
3. A baseball video game randomly assigns
positions to 9 players. What is the probability
that Lou, Manny, and Neil will be randomly
1
selected for the three-member outfield?
84
10-9 Probability of Compound Events
Lesson Quiz for Student Response Systems
1. Two number cubes are rolled. What is the
probability that the sum of the two numbers will
be 1?
A.
0
B.
1
1
C.
6
1
D.
36
10-9 Probability of Compound Events
Lesson Quiz for Student Response Systems
2. Two number cubes are rolled. What is the
probability that the sum of the two numbers will
be 6?
A. 0
B. 1
1
C.
6
1
D.
36
10-9 Probability of Compound Events
Lesson Quiz for Student Response Systems
3. Two number cubes are rolled. What is the
probability that the sum of the two numbers will
be 11?
A. 0
B. 1
1
6
D. 1
36
C.