User:Martin Hogbin/MHP - Conditional with goats

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Car hidden behind Door 3 (100 cases) Car hidden behind Door 1 (100 cases) Car hidden behind Door 2 (100 cases) Car hidden behind Door 3 (100 cases) Car hidden behind Door 1 (100 cases) Car hidden behind Door 2 (100 cases)
Player initially picks Door 1
Player has picked Door 1 and the car is behind Door 3 Player has picked Door 1 and the car is behind it Player has picked Door 1 and the car is behind Door 2 Player has picked Door 1 and the car is behind Door 3 Player has picked Door 1 and the car is behind it Player has picked Door 1 and the car is behind Door 2
Host must open Door 2 (100 cases) Host randomly opens Door 2 (50 cases) Host randomly opens Door 3 (50 cases) Host must open Door 3 (100 cases) Host randomly opens Door 3 (50 cases) Host must open Door 3 (100 cases)
Host must open Door 2 if the player picks Door 1 and the car is behind Door 3 Host opens Door 2 half the time if the player picks Door 1 and the car is behind it Host opens Door 3 half the time if the player picks Door 1 and the car is behind it Host must open Door 3 if the player picks Door 1 and the car is behind Door 2 Host opens Door 3 half the time if the player picks Door 1 and the car is behind it Host must open Door 3 if the player picks Door 1 and the car is behind Door 2 Host opens Door 3 half the time if the player picks Door 1 and the car is behind it Host must open Door 3 if the player picks Door 1 and the car is behind Door 2
Probability 1/3 (100 out of 300) Probability 1/6 (50 out of 300) Probability 1/6 (50 out of 300) Probability 1/3 (100 out of 300) Probability 1/6 (50 out of 300) Probability 1/3 (100 out of 300)
Switching wins Switching loses Switching loses Switching wins Switching loses Switching wins
If the host has opened Door 2, switching wins twice as often as staying (100 out of 150) If the host has opened Door 3, switching wins twice as often as staying (100 out of 150)
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