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hugeinc.com [email protected] 45 Main St. #220 Brooklyn, NY 11201 +1 718 625 4843 May 15, 2012 Standard presentation deck version 0.6
[email protected] Main St. #220 Brooklyn, NY 11201+1 718 625 4843
May 15, 2012Standard presentation deck version 0.6
Bayes’ Theorem
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
Monty Hall Problem.
Do you switch?
YES!
Switching increases your odds of
winning.
Weird, eh?
Visual explanation.
Bayes Theorem
P(A|B) =P(B|A)P(A)
P(B)
P(A|B) =P(B|A)P(A)
P(B)
P(A)= the probability of A
P(A|B) =P(B|A)P(A)
P(B)
P(B)= the probability of B
P(A|B) =P(B|A)P(A)
P(B)
P(A|B)= the probability of A given B
P(A|B) =P(B|A)P(A=1)
P(B)
P(A=1)= the probability of A equaling 1
P(A|B) =P(B=2|A=1)P(A)
P(B)
P(B=2|A=1)= the probability of B equaling 2 given A equals 1
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)
P(C=1|H=3,S=2)
P(C=1| S=2) = the probability that the Car is behind door
#1 and the Contestant selected door #2 = 1/3
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) x 1/3
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
Bayes’ applied.
P(H=3|C=1,S=2) P(C=1|S=2)
P(H=3|S=2)
1 x 1/3
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
Bayes’ applied.
P(H=3|C=1,S=2) P(C=1|S=2)
P(H=3|S=2)
1 x 1/3
1/2= 2/3!
Switching wins you a car 2/3 of the
time.
• Scientists
• Marketers
• Technologists
Who Cares?
Questions…
[email protected] Main St. #220 Brooklyn, NY 11201+1 718 625 4843
