Probability - part 1

The past 2 math classes have given me a lot to contemplate. I have been thinking tirelessly about a few of the activities Professor Antosz has brought up in class. The first being the card trick using 3 cards. The second being the birthday trick. Probability is a difficult strand to grasp, especially for younger students. Most individuals seem to have difficulty achieving the correct answers when dealing with probability. In the case of probability, logical deductions do not work as well. Thinking outside the box, or taking a alternate angle, in my opinion is the best option for obtaining the correct result.
One situation that Professor Antosz brought up in class was the 3 card game. The Professor help out 3 cards. 1 of the cards being the Ace of Spades. He showed us the Ace and then shuffled up the cards. He told us to pick one of the 3 cards (the Professor can see the 3 cards). We chose a card - either the Ace of Spades or 1 of the 2 other cards. At this point the Professor eliminates one of the other cards. Note that he will not eliminate the Ace of Spades. The reason being, that the Ace was possibly chosen by us on our original guess, and if not the Professor will keep it as the 2nd card left.  So now that there are only 2 cards left the Professor asks us if we want to switch cards, from our original choice to go with the only other card left, or to stick with our original selection? He gave us a few minutes to figure out the answer.
I immediately thought that I was smarter than this game and said 50-50 chance its the card we chose in the first place, so I said lets stick with it....I was told to reflect further. Upon further reflection I realized that the odds of selecting the Ace of Spades out of 3 cards only results in a 33% chance. Whereas, when you are left with 2 cards. (1 being the Ace of Spades) the card that was originally chosen is still sitting with a 33% odd of being the Ace of Spades, whereas the other card remaining has a 50% chance of being the Ace of Spades.
Resulting in the correct answer being -> you always pick the other card remaining, because of the better odds!!!!
In a group we attempted this experiment 20times. We always switched to the last card remaining. 14 of the 20 times we were correct and chose the Ace of Spades. The other 6 times we were incorrect, with the reason being that we selected the Ace on our first guess (with only 33% odds). Thus, in playing the odds we switched from the Ace of Spades (with poorer odds) to the other remaining card. (better odds)
As you can see, it can be rather difficult when trying to explain. Especially to our younger students. There are students who will be able to grasp this without difficulty, in that case I would have other probability problems ready for them to attempt while I would repeat the experiment for those still struggling with the concept.
Going back over this concept, you can see why it has had me thinking the past few weeks. Probability is difficult but not impossible. We as teachers need to open and willing to teach it. There is no need to be scared and shy away from material that we are not confident in. The more we try, the more we learn, and the better we can become as teachers.