Transcript 4.9 Compound Eventsx - Minidoka County Schools

I can...determine 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?
I can...determine probability of COMPOUND events!
Problem of the Day
ANSWER
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
I can...determine probability of COMPOUND events!
I will…
Learn to find
probabilities of
compound events.
I can...determine probability of COMPOUND events!
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.
I can...determine 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
I can...determine probability of COMPOUND events!
Practice 1 – Use 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.
I can...determine probability of COMPOUND events!
Continued Practice 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
I can...determine probability of COMPOUND events!
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.
I can...determine probability of COMPOUND events!
Continued Example 2
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
I can...determine probability of COMPOUND events!
Practice 2 – Using 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.
I can...determine probability of COMPOUND events!
Continued Practice 2
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
.
I can...determine probability of COMPOUND events!
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
I can...determine probability of COMPOUND events!
Practice 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
I can...determine probability of COMPOUND events!
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
I can...determine 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?
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. A baseball video game randomly assigns
positions to 9 players. What is the probability
that Lou, Manny, and Neil will be randomly
selected for the three-member outfield?
I can...determine 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
1
Wednesday?
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
ANSWERS
I can...determine 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
I can...determine 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
I can...determine 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.