# 14

Suppose I have a deck of four cards:  The ace of spades, the ace of hearts, and two others (say, 2C and 2D).

You draw two cards at random.

Scenario 1:  I ask you "Do you have the ace of spades?"  You say "Yes."  Then the probability that you are holding both aces is 1/3:  There are three equiprobable arrangements of cards you could be holding that contain AS, and one of these is AS+AH.

Scenario 2:  I ask you "Do you have an ace?"  You respond "Yes."  The probability you hold both aces is 1/5:  There are five arrangements of cards you could be holding (all except 2C+2D) and only one of those arrangements is AS+AH.

Now suppose I ask you "Do you have an ace?"

You say "Yes."

I then say to you:  "Choose one of the aces you're holding at random (so if you have only one, pick that one).  Is it the ace of spades?"