Reply to thread

Message

<blockquote data-quote="2WS-Steve" data-source="post: 353913" data-attributes="member: 3289">I think the paradoxical bit about this puzzle is that both versions seem the same but give different answers; for example:Case 1You ask someone to show you a picture of one of their kids (or they volunteer to do so). They show you a picture of a son. &gt;&gt;&gt; 50% chance the other kid is also a son.Case 2You ask someone if they have a son. They show you a picture of a son.&gt;&gt;&gt; 67% chance that the other kid is a daughter.In both cases they respond in the exact same way and you appear to gain the exact same additional information. How could there possibly be a difference in the probability change?However, you don’t gain the same evidence. In case 2 you placed a restriction on the way they could answer; they had to show you a son if they had one and if they didn’t have son you’d know precisely what gender both their children were. For instance, if they showed a picture of a daughter in case 2 you’d know the other child was also a daughter. But if they did the same in case 1 you wouldn’t know if the other child was a daughter or a son.That might indicate that there’s a general rule that placing restrictions on the way one can answer a question increases the value of the evidence you gain. Perhaps when we think about it that should be obvious but it certainly doesn’t seem obvious. It seems like all that should matter is the actual physical evidence we receive.</blockquote>

[QUOTE="2WS-Steve, post: 353913, member: 3289"] I think the paradoxical bit about this puzzle is that both versions seem the same but give different answers; for example: Case 1 You ask someone to show you a picture of one of their kids (or they volunteer to do so). They show you a picture of a son. >>> 50% chance the other kid is also a son. Case 2 You ask someone if they have a son. They show you a picture of a son. >>> 67% chance that the other kid is a daughter. In both cases they respond in the exact same way and you appear to gain the exact same additional information. How could there possibly be a difference in the probability change? However, you don’t gain the same evidence. In case 2 you placed a restriction on the way they could answer; they had to show you a son if they had one and if they didn’t have son you’d know precisely what gender both their children were. For instance, if they showed a picture of a daughter in case 2 you’d know the other child was also a daughter. But if they did the same in case 1 you wouldn’t know if the other child was a daughter or a son. That might indicate that there’s a general rule that placing restrictions on the way one can answer a question increases the value of the evidence you gain. Perhaps when we think about it that should be obvious but it certainly doesn’t seem obvious. It seems like all that should matter is the actual physical evidence we receive. [/QUOTE]

Verification