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Quantitative
Methods
for
Lawyers
Probability &
Basic Statistics (Part 1)
Class #6
@ computational
computationallegalstudie...
Basic Probability
Probability is a measure of how likely it is for an event to
happen.
We name a probability with a number from 0 to 1.
If a...
If it is uncertain whether or not an event will happen, then
its probability is some fraction between 0 and 1 (or a
fracti...
Basic Probability
Die
Dice
Basic Probability
Die Assuming the Die is Fair
Probability that
(1) You will Roll a 5?
(2) Probability you will
Roll a 5 i...
Basic Probability
Die
Assuming the Die
is Fair ...
This is a Random
Event
Basic Probability
http://www.math.csusb.edu/faculty/stanton/m262/intro_prob_models/
intro_prob_models.html
Basic Probability2
3
4
5
6
7
8
9
10
11
12 Please Calculate the Frequency
http://ccl.northwestern.edu/netlogo/models/DiceSt...
Basic Probability
2 1 1/36
3 2 2/36
4 3 3/36
5 4 4/36
6 5 5/36
7 6 6/36
8 5 5/36
9 4 4/36
10 3 3/36
11 2 2/36
12 1 1/36
Basic Probability
Two Dice
When two events are statistically independent, it means
that knowing whether one of them occurs makes it
neither more prob...
Example: The number appearing on the upward face of
a die the first time it is thrown and that appearing on the
same die th...
Basic Probability:
Coins
What is the Prob of Heads v. Tails?
What is the Prob of TT?
What is the Prob of HHH,?
What is the...
This is
Binomial
Basic Probability
With A Deck of Cards
Note: the Probability Changes
when Each Card is Drawn
Poker / Blackjack
Basic Probability
A Deck of Cards
Basic
Probability
A Deck of Cards
1.	 A red card	 	 	 	 	 	 	 	
2.	 A spade	 	 	 	 	 	 	 	
3.	 Not a spade	 	 	 	 	 	 	 	
...
1.	 A red card	 	 	 	 	 	 	 	 26/52	 	 ½
2.	 A spade	 	 	 	 	 	 	 	 13/52		 ¼
3.	 Not a spade		 	 	 	 	 	 	 39/52	 	 ¾
4.	...
Life
Expectancy
Calculator
http://www.msrs.state.mn.us/
info/Age_Cal.htmls
Quick Primer
on
Set Theory
Let's say that our universe contains the numbers
1, 2, 3, and 4.
Let A be the set containing the numbers 1 and 2; that is,...
Let's say that our
universe contains the
numbers 1, 2, 3, and
4.
Let A  be the set
c o n t a i n i n g t h e
numbers 1 and...
Plot the Probability Distribution
for Two Dice
If You Need
Additional Assistance
Probability: mathematical theory that describes
uncertainty




Statistics: series of techniques for describing and
extrac...
The arithmetic mean (or average) is
the sum of a series dividing by how
many numbers you added together.
Sum of Series of Numbers
Total # of Numbers in the Series
________________________________________________________________...
Lets Talk About Notation ...
x1, x2, x3 x4 .... xn
5, 7, 11, 13 ....
x bar
the Nth Term
Called
Lets Talk About Notation ...
x1, x2, x3 x4 .... xn
5, 7, 11, 13 ....
x bar
the Nth Term
Called
Calculating Measures of
Central Tendency
Series 1: 0, 0, 0, 0, 50, 50, 100, 100, 100, 100
Series 2: 10, 20, 30, 40, 50, 50...
Measures of Central Tendency
The number that occurs most frequently is
the mode.
When numbers are arranged in numerical
or...
Measures of Central Tendency
Series 1: 0, 0, 0, 0, 50, 50, 100, 100, 100, 100
Series 2: 10, 20, 30, 40, 50, 50, 60, 70, 80...
Bi Modal Distribution
Bi Modal Distribution
With Other Measures of
Central Tendency
Range
Range is the difference between the largest
and smallest values in a set of values.
For example, consider the follow...
Range &
Interquartile Range
The interquartile range (IQR) is a measure of
variability, based on dividing a data set into
q...
Range &
Interquartile Range
The interquartile range (IQR) is a measure of
variability, based on dividing a data set into
q...
Visualizing Range & IQR
The Box and Whisker Plot
New York City
31.5 33.6 42.4 52.5 62.7 71.6 76.8 75.5 68.2 57.5 47.6 36.6
Houston
50.4 53.9 60.6 68.3 74.5 80.4 82.6 82.3 ...
Visualizing Range & IQR
The Box and Whisker Plot
From
Google
Images
Daniel Martin Katz
@ computational
computationallegalstudies.com
lexpredict.com
danielmartinkatz.com
illinois tech - chica...
Quantitative Methods for Lawyers - Class #6 - Basic Statistics + Probability - Part 1 - Professor Daniel Martin Katz
Quantitative Methods for Lawyers - Class #6 - Basic Statistics + Probability - Part 1 - Professor Daniel Martin Katz
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Quantitative Methods for Lawyers - Class #6 - Basic Statistics + Probability - Part 1 - Professor Daniel Martin Katz

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Quantitative Methods for Lawyers - Class #6 - Basic Statistics + Probability - Part 1 - Professor Daniel Martin Katz

  1. 1. Quantitative Methods for Lawyers Probability & Basic Statistics (Part 1) Class #6 @ computational computationallegalstudies.com professor daniel martin katz danielmartinkatz.com lexpredict.com slideshare.net/DanielKatz
  2. 2. Basic Probability
  3. 3. Probability is a measure of how likely it is for an event to happen. We name a probability with a number from 0 to 1. If an event is certain to happen, then the probability of the event is 1 and certain not to happen, then the probability of the event is 0. Coin Flip with a Fair Coin P(H) = .5 P(T) = .5 Basic Probability
  4. 4. If it is uncertain whether or not an event will happen, then its probability is some fraction between 0 and 1 (or a fraction converted to a decimal number). 0 1 Certain not to happen Equally likely to happen or not to happen Certain to happen 0% 50 % Chance 100%
  5. 5. Basic Probability Die Dice
  6. 6. Basic Probability Die Assuming the Die is Fair Probability that (1) You will Roll a 5? (2) Probability you will Roll a 5 if 5 has Just Been Rolled
  7. 7. Basic Probability Die Assuming the Die is Fair ... This is a Random Event
  8. 8. Basic Probability http://www.math.csusb.edu/faculty/stanton/m262/intro_prob_models/ intro_prob_models.html
  9. 9. Basic Probability2 3 4 5 6 7 8 9 10 11 12 Please Calculate the Frequency http://ccl.northwestern.edu/netlogo/models/DiceStalagmite
  10. 10. Basic Probability 2 1 1/36 3 2 2/36 4 3 3/36 5 4 4/36 6 5 5/36 7 6 6/36 8 5 5/36 9 4 4/36 10 3 3/36 11 2 2/36 12 1 1/36
  11. 11. Basic Probability Two Dice
  12. 12. When two events are statistically independent, it means that knowing whether one of them occurs makes it neither more probable nor less probable that the other occurs. the occurrence of one event occurs does not affect the outcome of the occurrence of the other event. Similarly, when we assert that two random variables are independent, we intuitively mean that knowing something about the value of one of them does not yield any information about the value of the other. Statistical Independence
  13. 13. Example: The number appearing on the upward face of a die the first time it is thrown and that appearing on the same die the second time, are independent. e.g. the event of getting a "1" when a die is thrown and the event of getting a "1" the second time it is thrown are independent. Statistical Independence
  14. 14. Basic Probability: Coins What is the Prob of Heads v. Tails? What is the Prob of TT? What is the Prob of HHH,? What is the Prob of HTT?
  15. 15. This is Binomial
  16. 16. Basic Probability With A Deck of Cards
  17. 17. Note: the Probability Changes when Each Card is Drawn Poker / Blackjack
  18. 18. Basic Probability A Deck of Cards
  19. 19. Basic Probability A Deck of Cards 1. A red card 2. A spade 3. Not a spade 4. An ace 5. Not an ace 6. The ace of spades 7. A picture card 8. A number card or ‘not a picture card‘ 9. A card that is either a heart or a club 10. A 4 or 5 but not a spade 11. An even numbered card
  20. 20. 1. A red card 26/52 ½ 2. A spade 13/52 ¼ 3. Not a spade 39/52 ¾ 4. An ace 4/52 1/13 5. Not an ace 48/52 12/13 6. The ace of spades 1/52 7. A picture card 12/52 3/13 8. A number card or ‘not a picture card’ 40/52 10/13 9. A card that is either a heart or a club 26/52 ½ 10. A 4 or 5 but not a spade 6/52 3/26 11. An even numbered card 20/52 5/13
  21. 21. Life Expectancy Calculator http://www.msrs.state.mn.us/ info/Age_Cal.htmls
  22. 22. Quick Primer on Set Theory
  23. 23. Let's say that our universe contains the numbers 1, 2, 3, and 4. Let A be the set containing the numbers 1 and 2; that is, A = {1, 2}. (Warning: The curly braces are the customary notation for sets. Do not use parentheses or square brackets.) Let B be the set containing the numbers 2 and 3; that is, B = {2, 3}. Then we have the following relationships, with pinkish shading marking the solution "regions" in the Venn diagrams:
  24. 24. Let's say that our universe contains the numbers 1, 2, 3, and 4. Let A  be the set c o n t a i n i n g t h e numbers 1 and 2; that is, A = {1, 2}. Let B  be the set c o n t a i n i n g t h e numbers 2  and 3; that is, B = {2, 3}.
  25. 25. Plot the Probability Distribution for Two Dice
  26. 26. If You Need Additional Assistance
  27. 27. Probability: mathematical theory that describes uncertainty 
 
 Statistics: series of techniques for describing and extracting useful information from data Probability Versus Statistics
  28. 28. The arithmetic mean (or average) is the sum of a series dividing by how many numbers you added together.
  29. 29. Sum of Series of Numbers Total # of Numbers in the Series _____________________________________________________________________________ Mean =
  30. 30. Lets Talk About Notation ... x1, x2, x3 x4 .... xn 5, 7, 11, 13 .... x bar the Nth Term Called
  31. 31. Lets Talk About Notation ... x1, x2, x3 x4 .... xn 5, 7, 11, 13 .... x bar the Nth Term Called
  32. 32. Calculating Measures of Central Tendency Series 1: 0, 0, 0, 0, 50, 50, 100, 100, 100, 100 Series 2: 10, 20, 30, 40, 50, 50, 60, 70, 80, 90, 100 Series 3: 55, 60, 75, 77, 80, 83, 83, 83, 88, 91, 93 Please Calculate the arithmetic mean
  33. 33. Measures of Central Tendency The number that occurs most frequently is the mode. When numbers are arranged in numerical order, the middle one is the median.
  34. 34. Measures of Central Tendency Series 1: 0, 0, 0, 0, 50, 50, 100, 100, 100, 100 Series 2: 10, 20, 30, 40, 50, 50, 60, 70, 80, 90, 100 Series 3: 55, 60, 75, 77, 80, 83, 83, 83, 88, 91, 93 Please Calculate the Median & Mode
  35. 35. Bi Modal Distribution
  36. 36. Bi Modal Distribution With Other Measures of Central Tendency
  37. 37. Range Range is the difference between the largest and smallest values in a set of values. For example, consider the following numbers: 1, 2, 4, 7, 8, 9, 11. For this set of numbers, the range would be 11 - 1 or 10.
  38. 38. Range & Interquartile Range The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles The interquartile range is equal to Q3 minus Q1
  39. 39. Range & Interquartile Range The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles The interquartile range is equal to Q3 minus Q1 Example: 0, 10, 20, 30, 40, 50, 50, 60, 70, 80, 90, 100
  40. 40. Visualizing Range & IQR The Box and Whisker Plot
  41. 41. New York City 31.5 33.6 42.4 52.5 62.7 71.6 76.8 75.5 68.2 57.5 47.6 36.6 Houston 50.4 53.9 60.6 68.3 74.5 80.4 82.6 82.3 78.2 69.6 61 53.5 San Francisco 48.7 52.2 53.3 55.6 58.1 61.5 62.7 63.7 64.5 61 54.8 49.4 Average Monthly Temp
  42. 42. Visualizing Range & IQR The Box and Whisker Plot From Google Images
  43. 43. Daniel Martin Katz @ computational computationallegalstudies.com lexpredict.com danielmartinkatz.com illinois tech - chicago kent college of law@

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