No, you can not. But one must distinguish two cases:

1, the probability as "to happen", which is of course always independently 1/2.

2, the probability as "to have already happened" in the whole event.

I think we are talking about 2 here.

Just think of it in my verson of the Snow white puzzle. When she woke up, how likely it happened to January 1st? Very unlikely, wasn't it?

 

所有跟帖： 

• 明白您的意思，但那是醒来的概率，不是硬币朝上的概率，不是吗？ -露重烟微- ♀ (0 bytes) () 11/10/2023 postreply 14:14:00

• As part of the event they are no longer independent (case 2) -中间小谢- ♂ (110 bytes) () 11/10/2023 postreply 14:19:51

• 是的，这也是一个我当初很困惑的点，让我一度转成了1/2和1/3派。也就是像您列的，认为问题的问法有歧义。 -露重烟微- ♀ (0 bytes) () 11/10/2023 postreply 15:05:00

• 不过后来发现还是1/2，这里我先买个关子，看还有没有更多人想讨论的。 -露重烟微- ♀ (0 bytes) () 11/10/2023 postreply 15:08:00