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Mar
5
comment The frog puzzle
@A.S. While certainly not satisfying, I guess I can appreciate what you're saying.
Mar
5
comment The frog puzzle
I guess the main problem (which this answer does point out) is the interpretation of what "chances of survival" actually means. It's not tied to the actual situation but the information you have about it. It kind of helps to also consider that if I closed my ears I'd think my odds were even higher.
Mar
5
comment The frog puzzle
@A.S. Why do you insist that there has to be some method by which the information is acquired? The guy just KNOWS the gender of the frogs. He points at a male one. If both are male, he points at one at random. If both are male HE KNOWS both are male. It doesn't take him any more or less time and it certainly doesn't affect anything else in the universe. He just decides to point at one of them at random. A 50-50 chance.
Mar
5
comment The frog puzzle
@A.S. This is all irrelevant. You can imagine that another person behind you pointed at one male frog and said that it's male. You just didn't see which one he pointed at. There's no process. This just happened and this is your universe. If both were male he'd pick one at random. You can run the odds and see that without knowing which one he pointed at there's a 2/3 chance, and with knowing the extra info there's a 1/2 chance.
Mar
5
comment The frog puzzle
I think this is approaching the problem at the wrong time. A frog croaked, you turned around and now you're calculating your current chances of survival.
Mar
5
comment The frog puzzle
@A.S. I guess it would pick one of two at random and say that one is male.
Mar
5
comment The frog puzzle
@A.S. Well, the radar interpretation kind of masks the problem since it requires you to pick one frog to point at. To stay true to the problem we could say that it seems odd that upgrading the radar gun so it can tell you WHICH frog is male out of two of them somehow seems to decrease your odds of survival.
Mar
5
comment The frog puzzle
@abdefghijklmnopqrtxyz-stoo I explained why this isn't the case.
Mar
5
comment The frog puzzle
@A.S. The problem statement really wasn't that vague. I take slight offense to that. Any kind of story-based statement of a problem is inherently open to nit picks. Picking the most obvious model is assumed.
Mar
5
comment The frog puzzle
In other words. If I knew that the first ticket was blue, it would only serve to benefit me since I could pick it. Yes, seeing that the ticket it blue adds information that would benefit me, but removing a ticket from the pool has a much worse effect.
Mar
5
comment The frog puzzle
@A.S. I'm not sure what you're asking here. This is a hypothetical, theoretical scenario.
Mar
5
comment The frog puzzle
Right. I still don't think this is a valid argument. A person picking a ticket removes it from the pool and alters the system. The frogs don't change gender and my turning around certainly doesn't either.
Mar
5
comment The frog puzzle
If I had a $1/4$ chance of survival and now I have a $1/3$ then surely my chances haven't dropped but increased.
Mar
5
comment The frog puzzle
@GregMartin If the initial four combinations are equally likely, then removing one leaves three equally likely possibilities.
Mar
5
comment The frog puzzle
You lick both frogs. Now just one of them. The only choice is if you go for the singled out frog or the two behind you.
Mar
5
comment The frog puzzle
@GregMartin On one hand I'd say that we can assume independence here, on the other hand, it's assumptions like these that often break intuition.
Mar
5
asked The frog puzzle
Jan
10
awarded  Yearling
Oct
3
accepted Prove that no tangent in a convex shape crosses the interior
Oct
3
comment Prove that no tangent in a convex shape crosses the interior
Your last comment finally made it click. I'm accepting the answer.