When the going gets weird, the weird turn pro. - Hunter S. Thompson

08 April 2008

Perception of the doors

"My only advice is, if you can get me to offer you $5,000 not to open the door, take the money and go home." - Monty Hall (interviewed by John Tierney in the New York Times in 1991)

Explanation here:

There is no car behind Door 3, since the host opened it, so the last term must be zero. This can be proven using Bayes' theorem and the previous results:

\begin{align} P(C_3|H_{13},\,I) &= \frac{P(H_{13}|C_3,\,I)\,P(C_3|I)}{P(H_{13}|I)} \\  &= \left(0\times\frac13\right) /\, \frac12 = 0\ . \end{align}


P(C_2 | H_{13},\,I) = 1 - \frac13 - 0 = \frac23 .
This shows that the winning strategy is to switch the selection to Door 2.
Hat tip: Carrie

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