Probability

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Probability

• Prediction and Probability
• Counting Methods
• - Tree Diagrams
• - Organized List
• Factorials
• Adding Probabilities
• Multiplying Probabilities

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QUIZ
Probability
You have a jar with 12 blue marbles, 5 red
marbles and 3 white marbles. If you put your
hand in the jar, what are the chances of getting
a white marble? chances of getting a white
marble 3 total number of marbles
20 What are the chances of getting a blue
marble? chances of getting a white marble
12 3 total number of marbles 20 5
Probability this describes the likelihood that
an event will occur. Impossible Event the
chances of this event happening are 0. It will
never happen. Certain Event The chances of this
happening are 100. It will happen.
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Counting Methods
There are many different methods used to show the
possibility of combinations. You can use a tree
diagram, and organized list, or the counting
principle. Counting Principle If Diana has 3
shirts, 2 pairs of shoes and 5 pairs of pants,
how many different combinations are there? You
can use multiplication to find out 3 Shirts x
2 pairs of shoes x 5 pants 30 combinations
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Independent Events
QUIZ
Independent Events are events that may occur, but
one has nothing to do with the other. Janie has
three shirts red, white and blue. She also
has two pairs of pants green and black. How
many different combinations can she make? Make
a tree diagram to see all of the different
outfits Janie can wear.
RED, GREEN RED, BLACK WHITE, GREEN WHITE,
BLACK BLUE, GREEN BLUE, BLACK
There are six different combina-tions!
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• Michael has 10 cards with the letters A E I O
  U A E I O U on them. Answer the following
  questions based on this information.
• What is the probability that Michael will pick an
  A?
• 2/10 b. 1/5 c. 0/10
  d. 2/8
• What is the probability that Michael will pick an
  O or an I?
• 2/5 b. 0/10 c. 6/10 d. 4/10
• What is the probability that Michael will pick a
  consonant?
• a. 10/10 b. 2/10 c. 1/5 d. 0

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Organized List
How many different combinations can you make for
the following? Drink Sandwich Dessert Coke
Turkey Cake Juice Ham Pie Organized
List Coke, Turkey, Cake Juice, Turkey,
Cake Coke, Turkey, Pie Juice, Ham, Pie Coke,
Ham, Cake Juice, Ham, Cake Coke, Ham,
Pie Juice, Ham, Pie
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Factorials
Example 1 4! 4 x 3 x 2 x 1
24 Example 2 3! 4! 3 x 2 x 1
6 4 x 3 x 2 x 1
24 24 6 30 Example 3 3! -
2! 3 x 2 x 1 6 2 x 1
2 6 - 2 4
More Examples
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More Factorials
Example 4 3! X 4! 3 x 2 x 1 6 4 x
3 x 2 x 1 24 24 x 6 144 Example 4 9! 9
x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 4 4 x 3 x
2 x 1 Cancel out 4 x 3 x 2 x 1 9 x 8 x 7
x 6 x 5 15, 120
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Adding Probabilities
A A E I O U I P Use the above letters. What is
the probability of picking an A OR a P from
above? P (A) 2/8 P (P) 1/8 The
word OR indicates adding probabilities Add these
two fractions together. 2/8 1/8
3/8
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Multiplying Probabilities
A A E I O U I P The above cards are placed in a
bag. Independent Events A card is picked and
put back in the bag. What is the probability of
getting an I and then an O? P (I) 2/8 P
(O) 1/8 2/8 x 1/8 2/64 1/32
Dependent Events A card is picked and not
replaced in the bag. What is the probability of
getting an I and then an O? P (I) 2/8 P
(O) 1/7 2/8 x 1/7 2/56 1/28
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Janet has the choice of reading a mystery book,
horror book, biography or romance novel while on
her summer vacation. She will either go to
California, Florida, Texas or Colorado on her
summer break. Make a tree diagram of all the
possibilities. After drawing your tree diagram,
click here to see if you are correct!

• 1. How many different combinations can be made
  using the above information?
• a. 4 b. 8 c. 16
  d. 12
• 2. What is the probability that Janet will
  choose a mystery book AND go to Florida?
• a. ¼ b. 1/16 c. 1/8
  d. 0
• What is the probability that Janet will choose
  either a mystery book or a horror book and go to
  California or Texas?
• a. ½ b. 4/16 c. 8/16 d.
  ¼

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California Texas Colorado Florida
Mystery, California Mystery, Texas Mystery,
Colorado Mystery, Florida
Mystery Biography Horror Romance
California Texas Colorado Florida California Texa
s Colorado Florida
Biography, California Biography, Texas Biography,
Colorado Biography, Florida
Horror, California Horror, Texas Horror,
Colorado Horror, Florida
Romance, California Romance, Texas Romance,
Colorado Romance, Florida
California Texas Colorado Florida
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• James got the following test scores throughout
  his sixth grade career
• 67 68 98 65 87 74 89
  90 95 62
• 76 76 76 82 82
  76 77 90 98 94
• Make a Stem and Leaf plot and then check your
  answers here!
• What was the mode?
• a. 76 b. 90 c. 98 d. 90 and 98

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