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:

Hence:

.

This shows that the winning strategy is to switch the selection to Door 2.

Hat tip: Carrie