So intuitively my brain is like "1/2" but probably this Problem wouldn't be a Problem if that were true so I kept thinking (although it could be a level given the thread it's posted in). Couldn't get away from the 1/2 answer until I started writing things down, at which point 1/3 being the correct answer immediately became apparent. However, my brain still really wants the answer to be 1/2, so I kept thinking on it in case it was somehow some kind of tortoise and arrow trick.
When I asked myself what about coinflips, you flip two coins and one is heads, what're the chances the other is also heads, my brain is perfectly happy to accept 1/3 and sees that as logical and intuitive.
So now I'm sitting here wondering if the reason I can accept the cointoss but still cannot properly accept the puppyfire is that when the former was presented to me my gut (snap-reaction) said 1/2, whereas when the latter was presented to me I already knew the correct answer and so my gut (snap-reaction) said 1/3.
Really I'm just posting this whole thing because it alarms me if my brain is willing to betray me like this - hang onto something that it knows is wrong just because it was its first feeling on the matter.
edited to add: a) thanks for posting! and b) it's also possible the cointoss thing is easier for me (and others?) to see through because it's so easy to contrast "I flip two coins and one is heads, ..." with "I flip a coin and it's heads. I flip it again, ..."
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