Download Probability of Compound Events

11-8A Probability of Compound
Events
Jodie checks the online orders for a local
pizza parlor. The pizza parlor offers six
probabilities of
compound events using
different pizza toppings: anchovies,
organized lists, tables, or mushrooms, olives, onions, pepperoni,
tree diagrams.
and sausage. What is the probability that
the next two orders for a two-topping
pizza will be sausage and mushroom?
Learn to find
Tim Hawley/Foodpix/Getty Images
You can find the probability of compound events
using organized lists, tables, and tree diagrams.
EXAMPLE
1
Using an Organized List to Find Probability
U
A pizza parlor offers six different pizza toppings: anchovies,
mushrooms, olives, onions, pepperoni, and sausage. What is the
probability that a random order for a two-topping pizza will be
mushroom and sausage?
Let A ⴝ anchovies, M ⴝ mushrooms, Ol ⴝ olives, On ⴝ onion,
P ⴝ pepperoni, and S ⴝ sausage. List all possible two-topping pizzas.
Because the order of the toppings does not matter, you can eliminate
repeated pairs.
Anchovies-M
Anchovies-Ol
Anchovies-On
Anchovies-P
Anchovies-S
Mushroom-A
Mushroom-Ol
Mushroom-On
Mushroom-P
Mushroom-S
Olives-A
Olives-M
Olives-On
Olives-P
Olives-S
Onion-A
Onion-M
Onion-Ol
Onion-P
Onion-S
Pepperoni-A
Pepperoni-M
Pepperoni-Ol
Pepperoni-On
Pepperoni-S
Sausage-A
Sausage-M
Sausage-Ol
Sausage-On
Sausage-P
number of M&S pizzas
1
P(M&S) ⴝ _____ ⴝ _
total number of equally likely two-topping pizzas 15
The probability that a random two-topping order will be mushroom
1.
and sausage is __
15
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Chapter 11 Probability
EXAMPLE
2
Using a Tree Diagram to Find Probability
U
B
Bonnie,
Corrina, and Deanne line up in random order for softball
batting practice. What is the probability that the girls will line up
from front to back in alphabetical order?
Make a tree diagram showing possible line-up orders.
Let B Bonnie, C Corrina, and D Deanne.
B
C
D
C
D
BCD
D
C
BCD
B
D
CBD
D
B
CDB
B
C
DBC
C
B
DCB
List permutations beginning with
Bonnie.
List permutations beginning with
Corrina.
List permutations beginning with
Deanne.
number of line-ups in alphabetical order 1
P(alpha order) ____ _
6
total number of equally likely line-ups
The probability that the girls randomly line up in alphabetical
order is __16.
EXAMPLE
3
FFinding the Probability of Compound Events
J rolls two number cubes. What is the probability that the sum
Jen
of the two numbers will equal 5?
Make a table of all possible outcomes in the sample space.
1
2
3
4
5
6
1
1-1
1-2
1-3
1-4
1-5
1-6
2
2-1
2-2
2-3
2-4
2-5
2-6
3
3-1
3-2
3-3
3-4
3-5
3-6
4
4-1
4-2
4-3
4-4
4-5
4-6
5
5-1
5-2
5-3
5-4
5-5
5-6
6
6-1
6-2
6-3
6-4
6-5
6-6
Circle all
the pairs of
numbers that
have a sum
of 5.
There are 4 out of 36 possible outcomes that have a sum of 5.
4 __
1 , or about 11%.
The probability of rolling a sum of 5 is __
36
9
Think and Discuss
1. Explain how organized lists, tree diagrams, and tables help find
the sample space in an experiment.
11-8A Probability of Compound Events
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11-8A
Exercises
GUIDED PRACTICE
See Example 1
1.
Paula
1 Kai
K i and
dP
l are two of the five members of a singing group. Every week, the
group picks two names at random to sing a duet. What is the probability that
Kai and Paula will be chosen this week?
2. The seven houses on Kent Lane are numbered from 1 to 7. The local
newspaper chooses two of the houses at random to receive a free Sunday
paper. What is the probability that houses 6 and 7 receive the free paper?
See Example 2
3. Baby Deegan arranges alphabet blocks for the letters A, B, and T. What is the
probability that his arrangement spells a three-letter word?
4. At about 9:00 P.M. every night, flights from Chicago, Miami, and Denver
arrive at the local airport in a random order. What is the probability that the
Chicago flight will arrive first on any night?
See Example 3
5. Chaz rolls two number cubes. What is the probability that the sum of the two
numbers will be 7?
INDEPENDENT PRACTICE
See Example 1
6. A cafeteria
offers
carrots, peas, sweet potatoes, and broccoli.
f
ff
ffour vegetables:
b
The server prepares ready-to-go meals and puts two vegetables at random on
every plate. What is the probability that any randomly-chosen plate has peas
and broccoli?
7. For three nights in a row, Jared, Matt, and four other players play chess
against each other on the Internet. The computer randomly picks each
player’s opponent each night. What is the probability that Jared plays against
Matt on any night?
See Example 2
8. Letters A, R, T, and S are arranged in a random order. What is the probability
that the arrangement forms the words RATS, TARS, TSAR, or STAR?
9. Four aces are turned face down on a table, and two aces are drawn one after
the other. What is the probability that a the Ace of Hearts is drawn second?
See Example 3
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10. Sarah, David, and Ali are friends in science class. The teacher randomly
chooses two of the 12 students in the class to work together on a project.
What is the probability that two of these three friends will be chosen?
Chapter 11 Probability
PRACTICE AND PROBLEM SOLVING
11. M
11
Make
k a li
list off the
h ffour-letter
l
permutations
i
of the letters A, B, C, and
D. What is the probability of randomly choosing one of these
permutations?
Recreation
12. Make a list of the two-letter combinations of the letters A, B, C, D,
and E. What is the probability of randomly choosing one of these
combinations?
13. Recreation A deck of cards has 52 cards, four of which are aces. The
deck is shuffled, and the first four cards are turned over. What is the
probability that each card is an ace?
As playing cards
became popular,
different cultures
created their own
suits. The four suits
that are common
today—hearts, diamonds, spades, and
clubs—are from a
French design from
the 15th century.
14. The tree diagram shows the probability for randomly
choosing two dinner plates from a cabinet that contains
two blue plates and three yellow plates.
1st
2nd
Use the tree diagram to find the following probabilities:
a. Choosing two blue plates
b. Choosing a blue and yellow plate in any order
15. Write About It Explain how to create and use tables
to help solve a compound probability problem.
16. Challenge Cho, Darla, and four others are divided
randomly into two teams of three. What is the probability
that Cho and Darla are teammates?
Test Prep and Spiral Review
17. Multiple Choice Which expression shows the probability of choosing one
permutation at random from all the six-letter permutations of A, B, C, D, E, and F?
A
1
__
6
B
1
__
6!
C
6
___
10!
D
1
___
10!
18. Gridded Response For a history assignment, a teacher randomly chooses
three presidents from the first 10 presidents. The probability that Washington,
Madison, and Monroe are chosen is 1 out of what number?
Write each fraction as a percent. (Lesson 6-2)
19. __18
20. __35
9
21. __
20
8
22. __
25
25. x 121 200
26. 54 x 55
Solve each equation. (Lesson 1-10)
23. x 7 25
24. 15 x 100
11-8A Probability of Compound Events
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