Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Tim took one marble from a bag, recorded
the color, and returned it to the bag. He
repeated this several times and recorded the
results. 1. Find the experimental probability
that a marble selected from the bag will be
green. 2. Find the experimental
probability that a marble selected from the bag
will not be yellow.
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Problem of the Day What is the probability that
the sum of four consecutive whole numbers is
divisible by 4?.
0
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Learn to make an organized list to find all
possible outcomes.
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Vocabulary
sample space
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Sample spaces are used in finding probability.
The sample space for an experiment is all the
possible outcomes. You can use to show sample
spaces.
When you need to find many possible outcomes, you
can make a tree diagram. A tree diagram is one
way to organize information.
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Additional Example 1 Problem Solving
Application Matt wants to take a 3-day weekend
trip to visit his grandparents. He can take
either Friday or Monday off from work, and he can
either fly, drive, take a train, or take a bus.
How many options are available to Matt?
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Additional Example 1 Continued
List the important information

• Matt can take off either Friday or Monday.

• Matt can fly, drive, take a train, or take a bus.

You can draw a tree diagram to find all the
possible outcomes.
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Additional Example 1 Continued
Follow each branch on the tree diagram to find
all of the possible outcomes.
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Additional Example 1 Continued
Look Back
There are 8 different weekend trip combinations
available to Matt. There are 8 possible outcomes
listed.
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Check It Out Example 1 For her work uniform,
Missy has a choice of three colors of
pantsblack, khaki, or navy. She has four choices
for shirt colorsred, white, green, and yellow.
How many different uniforms can Missy wear?
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Check It Out Example 1 Continued
List the important information

• Missy has three colors of pants black, khaki, or
  navy.

• Missy has four colors of shirts red, white,
  green, and yellow.

You can draw a tree diagram to find all the
possible outcomes.
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Check It Out Example 1 Continued
black pants and red shirt black
pants and white shirt black pants and green shirt
black pants and yellow shirt
khaki pants and red shirt khaki pants and white
shirt khaki pants and green shirt khaki pants and
yellow shirt
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Check It Out Example 1 Continued
navy pants and red shirt navy pants
and white shirt navy pants and green shirt navy
pants and yellow shirt
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Check It Out Example 1 Continued
Look Back
There are 12 different uniform combinations
available to Missy. There are 12 possible
outcomes listed.
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Additional Example 2 Making an Organized List
One girl and one boy will be chosen to go to the
state science fair. The girl finalists are Alia,
Brenda, Cathy, Deb, and Erika. The boy finalists
are Frank, Greg, and Hal. How many different
pairs of one girl and one boy can be formed?
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Additional Example 2 Continued

• List all the pairs that begin with A. AF, AG, AH
• List all the pairs that begin with B. BF, BG, BH
• List all the pairs that begin with C. CF, CG, CH
• List all the pairs that begin with D. DF, DG, DH
• List all the pairs that begin with E. EF, EG, EH

There are 5 groups of 3 pairs.
3 3 3 3 3 15
There are 15 pairs of one girl and one boy.
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Check It Out Example 2 One girl and one boy will
be chosen to go to the movie preview. The girl
finalists are Fay, Gerri, Heidi, and Ingrid. The
boy finalists are Kevin, Larry, and Marc. How
many different pairs of one girl and one boy can
be formed?
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Check It Out Example 2 Continued

• List all the pairs that begin with F. FK, FL, FM
• List all the pairs that begin with G. GK, GL, GM
• List all the pairs that begin with H. HK, HL, HM
• List all the pairs that begin with I. IK, IL, IM

There are 4 groups of 3 pairs.
3 3 3 3 12
There are 12 pairs of one girl and one boy.
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Additional Example 3 Using the Fundamental
Counting Principle
Rick wants to buy a mammal and a reptile for
pets. The pet shop has dogs, cats, rabbits,
hamsters, and ferrets, which are all mammals. It
also has lizards, monitors, and boa constrictors,
which are all reptiles. How many combinations of
one mammal and one reptile are possible?
There are 5 choices for mammals and 3 choices for
reptiles.
Multiply the number of choices in each category.
5 3 15
There are 15 possible combinations.
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Check It Out Example 3
Tina wants to buy a sandwich and a drink. The
deli offers turkey, ham, tuna, and roast beef.
The deli offer water, soda, coffee, tea, and
juice for drinks. How many combinations of one
sandwich and one drink are possible?
There are 4 choices for sandwiches and 5 choices
for drinks.
Multiply the number of choices in each category.
4 5 20
There are 20 possible combinations.
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Lesson Quiz
1. A baseball coach has 4 pitchers, 3 catchers,
and 2 shortstops on his team. How many different
combinations of players can he use for the
positions? 2. You take 5 shirts, 3 pairs of
pants, and 2 pairs of shoes on vacation. How many
different outfits can you make? 3. You are
planning a small game booth at the local street
fair. You have a choice of 3 games and 4
different prizes. How many combinations of games
and prizes are there?
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30
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