May 15, 2012Standard presentation deck version 0.6hugeinc.cominfo@hugeinc.com45 Main St. #220 Brooklyn, NY 11201+1 718 625...
Bayes’ Theorem
Monty Hall Problem.Rules:• 3 doors• 1 door has a car• 2 doors have goats• After you select your door,  one door is opened ...
Do you switch?
YES!
Switching increasesyour odds of winning.
Weird, eh?
Visual explanation.
Bayes Theorem
P(B|A)P(A)P(A|B) =              P(B)
P(B|A)P(A)P(A|B) =                 P(B)P(A)= the probability of A
P(B|A)P(A)P(A|B) =                 P(B)P(B)= the probability of B
P(B|A)P(A)P(A|B) =                 P(B)P(A|B)= the probability of A           given B
P(B|A)P(A=1)P(A|B) =                 P(B)P(A=1)= the probability of A           equaling 1
P(B=2|A=1)P(A)P(A|B) =                  P(B)P(B=2|A=1)=the probability of Bequaling 2 given A equals 1
P(C=1|H=3,S=2)The probability that Car is behind door #1 given the Host opened door #3 and the Contestant selected door #2
P(C=1|H=3,S=2)
Bayes’ applied. P(H=3|C=1,S=2) P(C=1|S=2)                                         =        P(H=3|S=2)P(C=1| S=2) = the pro...
Bayes’ applied.  P(H=3|C=1,S=2) P(C=1|S=2)         P(H=3|S=2)• P(H=3|C=1,S=2) = the probability that Host opened door  #3 ...
Bayes’ applied.          P(H=3|C=1,S=2) P(C=1|S=2)                 P(H=3|S=2)• P(H=3|S=2) = the probability that Host open...
Switching wins you a car 2/3 of the time.
Who Cares?• Scientists• Marketers• Technologists
Questions…
hugeinc.cominfo@hugeinc.com45 Main St. #220 Brooklyn, NY 11201+1 718 625 4843
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  • PAUSE AND MAKE SURE PEOPLE UNDERSTAND PROBABILITY IS 1/3 FOR CAR
  • NO’S ARE IN COMPANY OF 1000 PHDS
  • Presentation presentation

    1. 1. May 15, 2012Standard presentation deck version 0.6hugeinc.cominfo@hugeinc.com45 Main St. #220 Brooklyn, NY 11201+1 718 625 4843
    2. 2. Bayes’ Theorem
    3. 3. Monty Hall Problem.Rules:• 3 doors• 1 door has a car• 2 doors have goats• After you select your door, one door is opened to reveal a goat• Given choice to switch
    4. 4. Do you switch?
    5. 5. YES!
    6. 6. Switching increasesyour odds of winning.
    7. 7. Weird, eh?
    8. 8. Visual explanation.
    9. 9. Bayes Theorem
    10. 10. P(B|A)P(A)P(A|B) = P(B)
    11. 11. P(B|A)P(A)P(A|B) = P(B)P(A)= the probability of A
    12. 12. P(B|A)P(A)P(A|B) = P(B)P(B)= the probability of B
    13. 13. P(B|A)P(A)P(A|B) = P(B)P(A|B)= the probability of A given B
    14. 14. P(B|A)P(A=1)P(A|B) = P(B)P(A=1)= the probability of A equaling 1
    15. 15. P(B=2|A=1)P(A)P(A|B) = P(B)P(B=2|A=1)=the probability of Bequaling 2 given A equals 1
    16. 16. P(C=1|H=3,S=2)The probability that Car is behind door #1 given the Host opened door #3 and the Contestant selected door #2
    17. 17. P(C=1|H=3,S=2)
    18. 18. Bayes’ applied. P(H=3|C=1,S=2) P(C=1|S=2) = P(H=3|S=2)P(C=1| S=2) = the probability that the Car is behind door #1and the Contestant selected door #2 = 1/3 P(H=3|C=1,S=2) x 1/3 P(H=3|S=2)
    19. 19. Bayes’ applied. P(H=3|C=1,S=2) P(C=1|S=2) P(H=3|S=2)• P(H=3|C=1,S=2) = the probability that Host opened door #3 given the Car was behind door #1 and the Contestant selected door #2 = 1 1 x 1/3 P(H=3|S=2)
    20. 20. Bayes’ applied. P(H=3|C=1,S=2) P(C=1|S=2) P(H=3|S=2)• P(H=3|S=2) = the probability that Host opened door #3 given the Contestant selected door #2 = 1/2 1 x 1/3 1/2 = 2/3!
    21. 21. Switching wins you a car 2/3 of the time.
    22. 22. Who Cares?• Scientists• Marketers• Technologists
    23. 23. Questions…
    24. 24. hugeinc.cominfo@hugeinc.com45 Main St. #220 Brooklyn, NY 11201+1 718 625 4843
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