Transcript Compound events

10-9 Probability of Compound Events
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
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
I can 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