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
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!