hugeinc.cominfo@hugeinc.com45 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…

hugeinc.cominfo@hugeinc.com45 Main St. #220 Brooklyn, NY 11201+1 718 625 4843