Quote:

The overwhelming (to me, at least) paradox of "the laws of chance" dictate that on each selection you have an equal chance of making the correct (or incorrect) choice.
I see the logic involved in changing from 1 out of 3 to 50%.



Let's try this little thought experiment:

We have three cards. An ace and two deuces. I shuffle the cards around and lay them out on the table. You choose one card that you think is the ace. What are your chances of being right?

If you said 1 in 3, congratulations, you're correct.

Now, I (knowing which card is the ace, because I peeked) touch one of the other two cards. What are your chances of having selected the ace on your first try?

If you said 1 in 3, congratulations. Nothing has changed, so your chances are still the same.

Now, I turn that card over, showing a deuce. What are your chances of having been correct on your first try?

If you said 1 in 2, please explain what has changed. Remember, I can always turn over a deuce. If you said 1 in 3, congratulations. Nothing has changed except you now know that one of the cards you didn't choose was a deuce. The chances of your first guess being correct are still 1 in 3. If you have two cards to choose from and one of them has a 1 in 3 chance of being the ace, what are the chances of the other being an ace?

The answer is left as an exercise for the student.