1. The Cartoon Guide to Statistics
Chapter 3: Probability
The Cartoon Guide to Statistics
By Larry Gonick
As Reviewed by:
Michelle Guzdek
GEOG 3000
Prof. Sutton
1/24/2010

2. It all started with gambling…
No one knows when it started, but it at least goes as far back as Ancient Egypt.
The Roman Emperor Cladius
(10BC – 54 AD) wrote the first
book on gambling.
Dice grew popular in the
Middle Ages.
GEOG 3000 – M. Guzdek
1/24/2010

3. Basic Definitions
Random Experiment – the process of observing the outcome of a chance event.
Elementary Outcome – all possible results of the random experiment.
Sample Space – the set or collection of all the elementary outcomes.
GEOG 3000 – M. Guzdek
1/24/2010

4. Coin Toss Example
The random experiment consists of recording the outcome.
The elementary outcomes are heads and tails.
The sample space is
the set written as {H,T}.
GEOG 3000 – M. Guzdek
1/24/2010

5. Sample Space For a single die For a pair of dice GEOG 3000 – M. Guzdek
1/24/2010

6. Probability
Probability is a numerical weight assigned to a possible outcome.
In a fair game of heads and tails, the outcomes are equally likely so probability is .5 for both.
P(H) = P(T) = .5
For two dice, there are 36 elementary outcomes – all equally likely.
P(BLACK 5, WHITE 2) = (1/6)*(1/6) = 1/36
GEOG 3000 – M. Guzdek
1/24/2010

7. Probability Histogram
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8. Probability Histogram
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9. What if…
What if things were not equal and a gambler throws loaded die?
Now P(1) = .25, and the remaining probabilities must equal = .75.
It 2,3,4,5, and 6 are equally likely to occur the probability of each is:
.75/5 = .15
P(x) =
GEOG 3000 – M. Guzdek
1/24/2010

10. Random Experiment Probabilities are never zero.
A probability of zero means it cannot happen.
Less than zero would be meaningless.
Therefore:
P(Oi) ≥ 0
If an event is certain to happen we assign probability of 1.
Combine these two and you have the Characteristic Properties of Probability
P(O1) + P(O2) + … + P(On) = 1
GEOG 3000 – M. Guzdek
1/24/2010

11. Approaches to Probability
Classical Probability
Based on gambling ideas.
Assumption is the game is fair and all elementary outcomes have the same probability.
Relative Frequency
When an experiment can be repeated, then an event’s probability is the proportion of times the event occurs in the long run.
Personal (Subjective) Probability
Life’s events are not repeatable.
An individual’s personal assessment of an outcome’s likelihood. For example, betting on a horse.
GEOG 3000 – M. Guzdek
1/24/2010

12. Modeled Probability vs. Relative Frequency
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1/24/2010

13. Basic Operations An EVENT is a set of elementary outcomes.
The probability of an event is the sum of the probabilities of the elementary outcomes in the set.
You can combine events to make other events, using logical operations.
AND, OR or NOT
GEOG 3000 – M. Guzdek
1/24/2010

14. Event: Dice Add to 7
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15. Calculate the events
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16. Answer
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1/24/2010

17. Calculate Probability
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18. Answer
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19. Addition Rule Mutually exclusive – not overlap
P(E OR F) = P(E) + P(F)
Overlap of elementary outcomes
P(E OR F) = P(E) + P(F) – P(E AND F)
When P(NOT E) is easier to compute use subtraction rule.
P(E) = 1 – P(NOT E)
GEOG 3000 – M. Guzdek
1/24/2010

20. Conditional Probability
The “probability of A, given C”
P(A|C) = P(E AND F)/P(F)
When E and F are mutually exclusive
P(E|F) = 0, once F has occurred E is impossible
Rearranging the definition get multiplication rule
P(E AND F) = P(E|F)P(F)
GEOG 3000 – M. Guzdek
1/24/2010

21. Independence
Two events E and F are independent of each other if the occurrence of one had no influence on the probability of the other.
P(E AND F) = P(E)P(F)
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1/24/2010

22. Bayes’ Theorem
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1/24/2010

23. References
DiFranco, Steven. Chapter 3: Probability Distributions,
Hajek, Alan. Interpretations of Probability, 2009.
Joyce, James. Bayes’ Theorem,
Khan Academy (YouTube Username: khanacademy). Probability (part 1),
Khan Academy (YouTube Username: khanacademy). Probability (part 5),
Spaniel, William (YouTube Username: JimBobJenkins). Game Theory 101: Basic Probability Rules,
Waner, Stefan and Steven Constanoble. 7.3: Probability and Probability Models,
Interactive quizzes
GEOG 3000 – M. Guzdek
1/24/2010