User:Martin Hogbin/sandbox

Ignore anything here.

In this instance of the game the host opened door 3 so door 3 is G

P(C=1,G=2,H=2) = 1/6 * P(H=2|C=1,G=2) = 1/6 (The revealed goat is goat 1)

P(C=1,G=2,H=3) = 1/6 * P(H=3|C=1,G=2) = 0

P(C=1,G=3,H=2) = 1/6 * P(H=2|C=1,G=3) = 0

P(C=1,G=3,H=3) = 1/6 * P(H=3|C=1,G=3) = 1/6

P(C=2,G=1,H=1) = 1/6 * P(H=1|C=2,G=1) = 0

P(C=2,G=1,H=3) = 1/6 * P(H=3|C=2,G=1) = 0

P(C=2,G=3,H=1) = 1/6 * P(H=1|C=2,G=3) = 0

P(C=2,G=3,H=3) = 1/6 * P(H=3|C=2,G=3) = 1/6

P(C=3,G=1,H=1) = 1/6 * P(H=1|C=3,G=1) = 0

P(C=3,G=1,H=2) = 1/6 * P(H=2|C=3,G=1) = 0

P(C=3,G=2,H=1) = 1/6 * P(H=1|C=3,G=2) = 0

P(C=3,G=2,H=2) = 1/6 * P(H=2|C=3,G=2) = 0