Unformatted text preview: B be the event that an empty door is opened. p ( A ) = 1 / 3. If the host knows where the gold is and open the empty door intentionally, then p ( B  A ) = 1, and p ( B ) = 1. So p ( A  B ) = p ( A ) p ( B  A ) /p ( B ) = 1 / 3. So one should switch. If the host does not know where the gold is, and he happens to open an empty door, then p ( B  A ) = 1, and p ( B  ¯ A ) = 1 / 2. So p ( B ) = p ( A ) p ( B  A )+ p ( ¯ A ) p ( B  ¯ A ) = 1 / 3 × 1+ 2 / 3 × 1 / 2 = 2 / 3. p ( A  B ) = p ( A ) p ( B  A ) /p ( B ) = 1 / 3 × 1 / (2 / 3) = 1 / 2, so there is no need to switch. 1...
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 Fall '09
 Wu

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