Transcript 6.1 use counting principles

1) In which year(s)
did the team lose
more games than
they won?
2) In which year
did the team play
the most games?
3) In which year
did the team play
ten games?
Number of Games
Warm-Up
10
8
Won
Lost
6
4
2
0
1
2
3
Year
4
6.1 The Addition &
Multiplication Principles of
Counting
What are we Learning Today?
Determine the number of
outcomes related to a
given event
Determine the number of outcomes related to a given event. Apply
the addition and multiplication principle of counting. Calculate and
use simple permutations and combinations.
The Addition Counting Principle
• If the outcome of interest can be divided
into groups with no possibilities in
common, then the number of possibilities
is the sum of the numbers of possibilities
in each group.
Determine the number of outcomes related to a given event. Apply
the addition and multiplication principle of counting. Calculate and
use simple permutations and combinations.
The Addition Counting Principle
Example:
• A box contains 5 bags of milk chocolate
M&M’s, 5 bags of peanut M&M’s, 5 bags
of sour skittles, 5 bags of regular skittles, 5
bags of chocolate covered raisins, and 5
bags of tropical skittles. How many bags
are a variety of skittles?
15
Determine the number of outcomes related to a given event. Apply
the addition and multiplication principle of counting. Calculate and
use simple permutations and combinations.
Tree Diagrams
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Tree diagrams allow
us to see all possible
outcomes of an event
and calculate their
probabilities.
This tree diagram
shows the
probabilities of
results of flipping
three coins.
Use an appropriate method to find the number of
outcomes in each of the following situations:
1. Your school cafeteria offers chicken or tuna sandwiches; chips
or fruit; and milk, apple juice, or orange juice. If you purchase
one sandwich, one side item and one drink, how many different
lunches can you choose? There are 12 possible lunches.
Sandwich(2)
Side Item(2)
chips
chicken
fruit
chips
tuna
fruit
Drink(3)
Outcomes
apple juice
orange juice
milk
apple juice
orange juice
milk
chicken, chips, apple
chicken, chips, orange
chicken, chips, milk
chicken, fruit, apple
chicken, fruit, orange
chicken, fruit, milk
apple juice
orange juice
milk
apple juice
orange juice
milk
tuna, chips, apple
tuna, chips, orange
tuna, chips, milk
tuna, fruit, apple
tuna, fruit, orange
tuna, fruit, milk
The Multiplication Counting Principle
• If one event can occur in m ways and another
event can occur in n ways, then the number of
ways that both events can occur together is
m∙n.
• In other words: Multiply the number of
choices you have at each stage
Determine the number of outcomes related to a given event. Apply
the addition and multiplication principle of counting. Calculate and
use simple permutations and combinations.
The Multiplication Counting Principle
Example:
2.) How many different looks can you give
Mr. Potato Head if we can choose from: 4
hats, 2 noses, 3 eyes, 2 shoes, and 5 ties?
240
Determine the number of outcomes related to a given event. Apply
the addition and multiplication principle of counting. Calculate and
use simple permutations and combinations.
Multiplication Counting Principle
3.) At a sporting goods store, skateboards are
available in 8 different deck designs. Each
deck design is available with 4 different
wheel assemblies. How many skateboard
choices does the store offer?
32
Multiplication Counting Principle
4.) A father takes his son Tanner to Wendy’s for
lunch. He tells Tanner he can get the 5 piece
nuggets, a spicy chicken sandwich, or a single
for the main entrée. For sides: he can get fries,
a side salad, potato, or chili. And for drinks: he
can get milk, coke, sprite, or the orange drink.
How many options for meals does Tanner
have?
48
Multiplication Counting Principle
5.) The combination for a briefcase consists of 3
symbols (letters and digits). How many
combinations are possible if at least one digit
is used?
Probability of an event
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The probability of event A is the number of
ways event A can occur divided by the total
number of possible outcomes.
P(A)=Favorable Outcome
Total Outcomes
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P(A)=Favorable Outcome
Total Outcomes (Choices)
6.) You and 2 friends each randomly pick a
movie from 6 choices. What is the probability
that you pick the same movie?
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P(A)=Favorable Outcome
Total Outcomes (Choices)
7.) A code consists of 3 digits (0-9).
a.) Find the probability that it starts with one.
b.) Find the probability that it only contains even
numbers.
c.) Find the probability that it uses the same
number in each position.
TICKET OUT THE DOOR
1.) Make a tree diagram that shows the total number of
choices for computer monitors:
Type: flat screen, flat panel
Size: 15 in., 17 in., 19 in., 21 in.
2.) Use the multiplication principle to answer:
You have 9 choices of curtains, 12 choices of paint & 18
choices of carpeting. How many different ways can
you decorate your room?
3.) The code to a safe is made up of 4 digits. What is the
probability that all 4 numbers are the same?
Homework
Session 1:
Pg. 340 1-13 all
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