All of Fraser's Comments + Replies

Fraser10

If the observer is distinct from Alice, absolutely. If the observer is Alice, nothing needs explaining in either case.

To put a bit of a crude metaphor on it, if you were to pick a random number uniformly between 0 and 1,000,000, and pre-commit to having a child on iff it's equal to some value X - from the point of view of the child, the probability that the number was equal to X is 100%.

Apologies if there's something more subtle with your answer that I've missed.

4Ape in the coat
Conditional P(X|X) = 1. However, unconditional P(X)  = 1/1,000,000.  Just like you can still reason about unconditional probability of a fair coin even after observing an outcome of the toss, the child can still reason about unconditional probability of their existence even after observing that they exist. They can notice it's very low, and therefore be rightfully surprised that they exist at all and update in favor of some hypothesis that would make their unconditional existence more likely.
Fraser10

If the only observable outcome is the one in which we got that extremely lucky, then it doesn't need explaining. You only can observe outcomes compatible with the fact of you making an observation.

2Ape in the coat
Suppose, someone comes to you and shows you a red ball. Then they explain that they had two bags one with all red balls and one with balls of ten different colors. They have randomly picked the bag from which to pick the ball and then randomly picked the ball from this bag. Additionally they've precommited to come to you and show you the ball iff it happened to be red. What are the odds that the ball that is being shown to you have been picked from the all-red bag?