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Probability

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... drawn at random from the cards shown. Write the probabilities as ... One card is drawn out of a standard deck of cards. Find: P(red) = P(red U black) = P(4 U 7) ... – PowerPoint PPT presentation

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Title: Probability


1
Probability
  • Youll probably like it!

2
Probability as a ratio
Probability of choosing an orange polygon from
below
3
Probability Properties Continued
  • The number line shows the range of probabilities
    between 0 and 1.
  • Probability can be written as a fraction,
    decimal, or percentage.
  • When using fractions, remember to reduce answers
    to lowest terms.

4
Probability - Some Definitions
  • The sample space of an experiment is the list of
    all possible outcomes.
  • An event is a set (collection) of one or more
    outcomes in the sample space.
  • An outcome is the result of an experiment or
    other situation involving uncertainty.

When rolling two standard dice the sum could be
either 2, 3, 4, 5, 6, 7, 8, 9, 10 , 11, or 12.
An event is the possibility of actually rolling
one or more of those totals Say event A is
rolling a sum of four
An outcome in this dice example is the sum you
actually rolled!
5
Probability Properties
  • The probability of an event, say event A, is
    denoted P(A).
  • All probabilities are between 0 and 1.
  • (i.e. 0 ? P(A) ? 1)
  • The sum of the probabilities of all possible
    outcomes must be 1.

6
Probability using equally likely outcomes
Each card is equally likely to be drawn from a
shuffled deck
Each face of a numbered cube is equally likely to
show up when rolling a die
Each face of a coin is equally likely to land up
when flipping
7
Find the probability of spinning the spinner once
and.
  • 1. Getting a 2 P(2)
  • Only one outcome 2
  • 2. Getting at least 2 P(at least 2)
  • Outcomes 2, 3, 4, or 5
  • 3. Getting more than 3 P(4 or 5)
  • Outcomes 4 or 5
  • 4. Getting a prime number P(prime)
  • Outcomes 2, 3, or 5
  • 5. Getting a number less than 10 P(less than
    10)
  • Outcomes 0, 1, 2, 3, 4, or 5

8
Lots of problems come from a standard deck of
cards so take a look at the sample space
9
Find the probabilities below
  • Flipping a coin and getting tails
  • Picking a diamond out of a deck of cards
  • Rolling a numbered cube (die) and getting a 5

Always reduce fractions!
10
Probabilities Using Relative Frequencies
  • A card is drawn at random from the cards shown.
    Write the probabilities as simplified fractions.

M
A
T
H
E
M
A
T
I
C
S
  • P(M)
  • P(V)
  • P(shaded)
  • P(vowel)
  • P(shaded and vowel)
  • P(shaded or a vowel)

11
Website Activity
  • Level 1 find the probability of choosing a red
    or yellow fish from the tank.
  • Level 2 add red or yellow fish to get a
    specific probability (answers as fractions)
  • Level 3 add fish to get a specific probability
    (answers given in decimals)
  • Fish Tank

12
Probability Notations Advanced Definitions
13
Complement
  • The complement of an event A, denoted by A, is
    the set of outcomes that are not in A
  • A means A does not occur
  • P(tails) P(heads)
  • Some books use Ac , A, or A
  • to denote the complement of A

14
Law of Complements
  • P(A) 1 P(A)
  • When drawing a card out of a deckP(king) 1
    P(king)

15
Notation ? versus ?
  • Combining two events together using the terms
    and or or
  • AND ?
  • P(Jack ? Heart) P(Jack and Heart)
  • OR ?
  • P(Jack ? Ace) P(Jack or Ace)

16
One card is drawn out of a standard deck of
cards. Find
  • P(red)
  • P(red U black)
  • P(4 U 7)
  • P(4 n 7)

0
17
Probability Using Events
  • A card is randomly drawn from a deck
  • Let A The card is a face card
  • Let B The card is black
  • Let C The card is a heart
  • Find the following probabilities
  • P(C)
  • P(A n B)
  • P(B U C)

18
Homework
  • Worksheet Basic Probability
  • Notations Definitions
  • Give the probabilities as reduced fractions

19
Other Websites
  • The next few pages have other probability
    activities you could use instead of the more
    traditional examples given in the PowerPoint
    presentation.

20
Experimental Probability with Spinners and Number
Cubes
  • Spinners Which color will the spinner land on
    the most?
  • Hit the New Spinner button to pick a spinner
    with a different number of spaces
  • Dice Which sum will come up the most often?
  • Shodor Interactive

21
Drawing numbers from a box
  • This activity will let us add any amount of
    numbered tiles into a box. Then we can draw
    random tiles (with replacement) to see how
    frequently each number gets picked.
  • Compare experimental results to theoretical
    results note the more draws you take, the
    closer these values get to each other.
  • Applet can run slowly one by one or use the
    quick draw to do a bunch all at once.
  • Box Model

22
Typing random letters
If a monkey were typing random letters into a
computer, is it possible real words and sentences
would be typed?
  • Is it possible for the monkey to write a line
    from Shakespeare? If so, how many letters would
    it take before we could read, To be or not to
    be?

Well yes it is possible, but it is very
unlikely!
23
Random Typing Activity
  • What if we just used the letters from TO BE OR
    NOT TO BE how many random letters would we
    have to type before we could form a word like
    BET?
  • What two-letter or three-letter word would be the
    most common?
  • Hamlet Happens

This may take a while so let this run while
starting assignment.
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