Argument 2 is correct. Showing an ace provides no relevant information. If you want to do the math, I like Blueberry’s solution. Or: if you have 2 aces, then your chances of saying “yes, it’s AS” are 50-50 since you were equally likely to have chosen either ace (you picked one at random), and if you have 1 ace, then your chances of saying “yes, it’s AS” are 50-50 since you are equally likely to have either ace, so your “yes” answer does not provide any information about how many aces you have.
Argument 1 is wrong because in Scenario 1 if you have the AS you are guaranteed to say “yes,” but in this case if you have AS you still might say “no,” so the information provided is not the same.
Argument 2 is correct. Showing an ace provides no relevant information. If you want to do the math, I like Blueberry’s solution. Or: if you have 2 aces, then your chances of saying “yes, it’s AS” are 50-50 since you were equally likely to have chosen either ace (you picked one at random), and if you have 1 ace, then your chances of saying “yes, it’s AS” are 50-50 since you are equally likely to have either ace, so your “yes” answer does not provide any information about how many aces you have.
Argument 1 is wrong because in Scenario 1 if you have the AS you are guaranteed to say “yes,” but in this case if you have AS you still might say “no,” so the information provided is not the same.