Title: Probability
1Probability
2Probability as a ratio
Probability of choosing an orange polygon from
below
3Probability 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.
4Probability - 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!
5Probability 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.
6Probability 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
7Find 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
8Lots of problems come from a standard deck of
cards so take a look at the sample space
9Find 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!
10Probabilities 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)
11Website 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
12Probability Notations Advanced Definitions
13Complement
- 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
14Law of Complements
- P(A) 1 P(A)
- When drawing a card out of a deckP(king) 1
P(king)
15Notation ? 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)
16One 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
17Probability 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
18Homework
- Worksheet Basic Probability
- Notations Definitions
- Give the probabilities as reduced fractions
19Other Websites
- The next few pages have other probability
activities you could use instead of the more
traditional examples given in the PowerPoint
presentation.
20Experimental 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
21Drawing 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
22Typing 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!
23Random 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.