description

1. May 15, 2012
Standard presentation deck version 0.6
hugeinc.com
info@hugeinc.com
45 Main St. #220 Brooklyn, NY 11201
+1 718 625 4843

2. Bayes’ Theorem

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. Do you switch?

5. YES!

6. Switching increases
your odds of winning.

7. Weird, eh?

8. Visual explanation.

9. Bayes Theorem

10. P(B|A)P(A)
P(A|B) =
P(B)

11. P(B|A)P(A)
P(A|B) =
P(B)
P(A)= the probability of A

12. P(B|A)P(A)
P(A|B) =
P(B)
P(B)= the probability of B

13. P(B|A)P(A)
P(A|B) =
P(B)
P(A|B)= the probability of A
given B

14. P(B|A)P(A=1)
P(A|B) =
P(B)
P(A=1)= the probability of A
equaling 1

15. P(B=2|A=1)P(A)
P(A|B) =
P(B)
P(B=2|A=1)=
the probability of B
equaling 2 given A equals 1

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. P(C=1|H=3,S=2)

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 #1
and the Contestant selected door #2 = 1/3
P(H=3|C=1,S=2) x 1/3
P(H=3|S=2)

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. 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. Switching wins you a
car 2/3 of the time.

22. Who Cares?
• Scientists
• Marketers
• Technologists

23. Questions…

24. hugeinc.com
info@hugeinc.com
45 Main St. #220 Brooklyn, NY 11201
+1 718 625 4843