Cookbooks

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Cookbooks!
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Patrick's Casino
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http//www.mendelsohn1.com81/java_example_1.html
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What is the probability of picking an ace?
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Probability
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What is the probability of picking an ace? 4 / 52
.077 or 7.7 chances in 100
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Every card has the same probability of being
picked
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What is the probability of getting a 10, J, Q, or
K?
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(.077) (.077) (.077) (.077) .308 16 / 52
.308
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What is the probability of getting a 2 and then
after replacing the card getting a 3 ?
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(.077) (.077) .0059
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What is the probability that the two cards you
draw will be a black jack?
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10 Card (.077) (.077) (.077) (.077)
.308 Ace after one card is removed 4/51
.078 (.308)(.078) .024
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Practice

• What is the probability of rolling a 1 using a
  six sided dice?
• What is the probability of rolling either a 1
  or a 2 with a six sided dice?
• What is the probability of rolling two 1s
  using two six sided dice?

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Practice

• What is the probability of rolling a 1 using a
  six sided dice?
• 1 / 6 .166
• What is the probability of rolling either a 1
  or a 2 with a six sided dice?
• What is the probability of rolling two 1s
  using two six sided dice?

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Practice

• What is the probability of rolling a 1 using a
  six sided dice?
• 1 / 6 .166
• What is the probability of rolling either a 1
  or a 2 with a six sided dice?
• (.166) (.166) .332
• What is the probability of rolling two 1s
  using two six sided dice?

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Practice

• What is the probability of rolling a 1 using a
  six sided dice?
• 1 / 6 .166
• What is the probability of rolling either a 1
  or a 2 with a six sided dice?
• (.166) (.166) .332
• What is the probability of rolling two 1s
  using two six sided dice?
• (.166)(.166) .028

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Cards

• What is the probability of drawing an ace?
• What is the probability of drawing another ace?
• What is the probability the next four cards you
  draw will each be an ace?
• What is the probability that an ace will be in
  the first four cards dealt?

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Cards

• What is the probability of drawing an ace?
• 4/52 .0769
• What is the probability of drawing another ace?
• 4/52 .0769 3/51 .0588 .0769.0588 .0045
• What is the probability the next four cards you
  draw will each be an ace?
• .0769.0588.04.02 .000003
• What is the probability that an ace will be in
  the first four cards dealt?
• .0769.078.08.082 .3169

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Probability
1.00
.00
Event must occur
Event will not occur
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Probability

• In this chapter we deal with discreet variables
• i.e., a variable that has a limited number of
  values
• Previously we discussed the probability of
  continuous variables (Z scores)
• It does not make sense to seek the probability of
  a single score for a continuous variable
• Seek the probability of a range of scores

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Key Terms

• Independent event
• When the occurrence of one event has no effect on
  the occurrence of another event
• e.g., voting behavior, IQ, etc.
• Mutually exclusive
• When the occurrence of one even precludes the
  occurrence of another event
• e.g., your year in the program

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Key Terms

• Joint probability
• The probability of the co-occurrence of two or
  more events
• The probability of rolling a one and a six
• p (1, 6)
• p (Blond, Blue)

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Key Terms

• Conditional probabilities
• The probability that one event will occur given
  that some other vent has occurred
• e.g., what is the probability a person will get
  into a PhD program given that they attended
  Villanova
• p(Phd l Villa)
• e.g., what is the probability that a person will
  be a millionaire given that they attended college
• p( l college)

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Example
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What is the simple probability that a person will
own a video game?
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What is the simple probability that a person will
own a video game? 35 / 100 .35
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What is the conditional probability of a person
owning a video game given that he or she has
children? p (video l child)
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What is the conditional probability of a person
owning a video game given that he or she has
children?25 / 55 .45
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What is the joint probability that a person will
own a video game and have children? p(video,
child)
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What is the joint probability that a person will
own a video game and have children? 25 / 100 .25
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25 / 100 .25.35 .55 .19
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The multiplication rule assumes that the two
events are independent of each other it does
not work when there is a relationship!
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Practice
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p (republican) p(female)p (republican,
male) p(female, republican)p (republican l
male) p(male l republican)
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p (republican) 70 / 162 .43p (republican,
male) 52 / 162 .32p (republican l male) 52
/ 79 .66
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p(female) 83 / 162 .51p(female, republican)
18 / 162 .11p(male l republican) 52 / 70
.74
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Foot Race

• Three different people enter a foot race
• A, B, C
• How many different combinations are there for
  these people to finish?

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Foot Race

• A, B, C
• A, C, B
• B, A, C
• B, C, A
• C, B, A
• C, A, B
• 6 different permutations of these three names
  taken three at a time

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Foot Race

• Six different people enter a foot race
• A, B, C, D, E, F
• How many different permutations are there for
  these people to finish?

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Permutation

• Ingredients
• N total number of events
• r number of events selected

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Permutation

• Ingredients
• N total number of events
• r number of events selected
• A, B, C, D, E, F Note 0! 1

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Foot Race

• Six different people enter a foot race
• A, B, C, D, E, F
• How many different permutations are there for
  these people to finish in the top three?
• A, B, C A, C, D A, D, E B, C, A

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Permutation

• Ingredients
• N total number of events
• r number of events selected

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Permutation

• Ingredients
• N total number of events
• r number of events selected

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Foot Race

• Six different people enter a foot race
• If a person only needs to finish in the top three
  to qualify for the next race (i.e., we dont care
  about the order) how many different outcomes are
  there?

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Combinations

• Ingredients
• N total number of events
• r number of events selected

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Combinations

• Ingredients
• N total number of events
• r number of events selected

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Note

• Use Permutation when ORDER matters
• Use Combination when ORDER does not matter

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Practice

• There are three different prizes
• 1st 1,00
• 2nd 500
• 3rd 100
• There are eight finalist in a drawing who are
  going to be awarded these prizes.
• A person can only win one prize
• How many different ways are there to award these
  prizes?

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Practice

• 336 ways of awarding the three different prizes

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Practice

• There are three prizes (each is worth 200)
• There are eight finalist in a drawing who are
  going to be awarded these prizes.
• A person can only win one prize
• How many different ways are there to award these
  prizes?

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Combinations

• 56 different ways to award these prizes

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Practice

• A shirt comes in four sizes and six colors. One
  also has the choice of a dragon, alligator, or no
  emblem on the pocket. How many different kinds
  of shirts can you order?

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Practice

• A shirt comes in four sizes and six colors. One
  also has the choice of a dragon, alligator, or no
  emblem on the pocket. How many different kinds
  of shirts can you order?
• 463 72
• Dont make it hard on yourself!

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Practice

• In the recent California Governor race there were
  135 candidates. The state created ballots that
  would list candidates in different orders. How
  many different types of ballots did the state
  need to create?

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Practice

• 2.6904727073180495e230
• Or

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• 26,904,727,073,180,495,000,000,000,000,000,000,00
  0,000,000,000,000,000,000,000,000,000,000,000,000,
  000,000,000,000,000,000,000,000,000,000,000,000,00
  0,000,000,000,000,000,000,000,000,000,000,000,000,
  000,000,000,000,000,000,000,000,000,000,000,000,00
  0,000,000,000,000,000,000,000,000,000,000,000,000,
  000,000,000

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Practice

• Page 137
• Exercise 5.2
• Exercise 5.3
• Exercise 5.4 and 5.5

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5.2

• p 1 / 1000 .001
• p 2 / 1000 .002
• p .001 .002 .003

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5.3

• p 1 / 9 .111
• p (2 / 10)(1/9) (.20)(.111) .022
• p (1/10)(2/9) (.10)(.22) .022
• p (.022)(.022) .044

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5.4

• p 1 / 9 .111
• p (2 / 10)(1/9) (.20)(.111) .022
• p (b win 1, y win 2)
• p (1/10)(2/9) (.10)(.22) .022
• p (y win 1, b win 1)
• p (.022)(.022) .044
• p(b win 1, y win 2) p (y win 1, b win 2)

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5.5

• p 1 / 9 .111
• p(win 2nd l lost1st)
• p (2 / 10)(1/9) (.20)(.111) .022
• p (1/10)(2/9) (.10)(.22) .022
• p (.022)(.022) .044

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Practice

• Page 139 --
• Exercise 5.26
• Exercise 5.27
• Exercise 5.28

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5.26
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5.27
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5.28
There are 60 possible orders to push 3 out of 5
buttons. The probability that the subject will
choose the correct order on the first trial is p
(1/60) .017
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Extra Brownie Points!

• Lottery
• To Win
• choose the 5 winnings numbers
• from 1 to 49
• AND
• Choose the "Powerball" number
• from 1 to 42
• What is the probability you will win?
• Use combinations to answer this question

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• p of winning jackpot
• Total number of ways to win / total number of
  possible outcomes

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Total Number of Outcomes

Different 5 number combinations
Different Powerball outcomes
Thus, there are 1,906,884 42 80,089,128 ways
the drawing can occur
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Total Number of Ways to Win

Only one way to win
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