OK, smarty-pants, what's the best move?

[surviva316]

some clicking landed me to this one, lets call it part 2 of the thread

A shopkeeper says she has two new baby beagles to show you, but she doesn't know whether they're male, female, or a pair. You tell her that you want only a male, and she telephones the fellow who's giving them a bath. "Is at least one a male?" she asks him. "Yes!" she informs you with a smile. What is the probability that the other one is a male?

Grunch, and I hadn't heard this before but I'm damn-near 100% certain this is correct:

EDIT: Apparently we're doing spoiler tags now.

Spoiler: Show

33% if they checked both dogs and concluded that at least one had a penis; 50% if they only looked at one and that one certainly had a penis, so we have 0 information on if the other one does.

All of the possible permuations are as follows:

1. Dog 1 has a penis and Dog 2 has a penis; (25%)
2. Dog 1 has a penis but Dog 2 does not have a penis; (25%)
3. Dog 1 does not have a penis but Dog 2 does; and (25%)
4. Neither has a penis. (25%)

In the scenario that the bather checks both dogs, at least one will have a penis 75% of the time (the aggregate of the first 3 permutations). Only one out of those three permutations (33% of the time within that subset), though, do both of the dogs have a penis.

In the scenario where the first dog they check has a penis, and then it's up in the air whether the second one does or not, we're talking exclusively about permutations 1 and 2. In one out of THOSE two permutations, Dog 2 has a penis, which makes sense because we've been given zero information whatsoever about the dog, so its nature's probability of penis-ownership is unchanged.

This one feels like less of a paradox. We pretty clearly get less information out of someone saying they checked multiple dogs and at least one of them was a male than we get out of checking one dog and find that it is male.

EDIT after reading responses:

Spoiler: Show

This may have been less of a mindfuck for me than it was for others to think it through methodically and find a different reaction. I think my various learning disabilities makes it so that I'm never surprised that thinking it through methodically gets me a different answer than the first one I blurt out, so I'm just like, "Surprise, surprise, my initial reaction was wrong like it so frequently is."

The Monty Hall problem, though, did fuck my mind for a long time just because it's SO counter-intuitive. It's much harder for me to wrap my brain around the concept of two doors' probabilities' combining than it is for me to wrap my head around the fact that we get weaker information from knowing that at least 1 out of 2 of the 50% probabilities are realized than we do out of knowing that 1 out of 1 of them are, so the chances of the 25% probability being realized are more marginally improved.