Just had quite a discussion with my co-workers on this one.
If we had a pile of four cards. A King of spades, King of Hearts, Ace of Spades, Ace of Hearts, I pick up two cards and look at them. I then tell you, truthfully, that AT LEAST ONE of the cards I have is an Ace. (Q1) What is the probability of my other card being the other ace? (Q2) If I told you that the card I had was an ace of spades, what is the probability of the other card being the ace of hearts?
Now, I'm quite certain that in either case, the possibility that the other card is 1/3. But my co-worker swears it is 1/5. Here is his logic:
If we permute on the possibilities (ignoring order), there can be 6 total possibilities:
If one of the cards is an Ace, then that eliminates the (Kh, Ks) pair. (Q1) Thus there is only a 1/5 chance that the other card is an ace. (Q2) If I knew the card was an ace of spades, then that eliminates 3 possibilities, leaving 3 possibilities, thus is 1/3 chance the other card is the ace of hearts.
My logic: This is incorrect because permuting on the cards' suit (Spades, Hearts), is not relevant to the question asked - doesnt matter how you arrange the suits, the number of possible win conditions do not change since the question only asks if the cards VALUE (Ace, king) are the same.
Help? Can anyone offer an understandable explanation?
I also created a small C# program to test a few examples of how I interpret the excercise. I'm getting fairly solid 1/3. If anyone cares to double check my implementations and point out any possible errors, that would be great. It can be found here (Runnable in browser) - https://repl.it/BsJ9/17