Re: interesting coin flip problem
Your teacher is right, and exactly for the reasons he stated.
There are two coins -- let's call them coin 1 and coin 2. You've been told that one of them comes up heads, but don't know which one.
When we started, there were four possibilities. The information given eliminates one and only one of the possibilities, so there's a 2/3 chance that the coin is heads.
This problem is kind of like the Monte Hall -- Let's Make a Deal problem.
In that show, contestents were given the opportunity to go for the "Big Deal" which was behind one of three Doors.
A contestant chooses Door Number 1. Monte (who knows where the loot really is) shows the contestant that the Big Deal was not behind Door Number 2, and then offers the contestent the chance to change his choice of doors (i.e., swap door 1 for door 3). What should the contestant do.
The answer -- Assuming that Monty would have shown a door and offered the contestant the swap in all circumstances, is that the contestant should swap. There's a 1/3 chance the Big Deal is behind door number 1, and a 2/3 chance it's behind door number 3.
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