What fraction of children would have no parents?

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This question has pop-culture origins but is mathematical for sure.

In the movie "Avengers: Infinity War" (SPOILERS AHEAD) the main villain eliminates half of all life on the Earth (technically the universe, but let's just assume it was the Earth for this question). I was reading an article about the following movie dealing with the ramifications of this, and it was mentioned that a deleted scene had focused on what happened to the children in this scenario. Specifically, the article claimed that $0.25$ of children on Earth would become parent-less. I believe their reasoning was that since each parent has a $0.5$ chance of disappearing the final probability for missing both parents would be $0.5\times0.5=0.25$. The issue I have with this is that many children have siblings. So for example if a family with three children had both parents disappear, then that is three counts of no parents, not just one count.

I think the correct statement would be $0.25$ of families would end up with both parents gone. However, this then got me thinking about what would actually be the probability for a single child to lose both of their parents when taking into account families with multiple children. I would think that the answer to this question would depend on the distribution of number of children in a family on Earth. But given this distribution how would we then determine this fraction of children who lose both of their parents if half of all people suddenly disappeared?

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The number of children in a family is not an issue. One way to see it is just consider the $n$ child families. By the same calculation, $\frac 14$ of those families will lose both parents, so $\frac 14$ of the children in $n$ child families lose both parents. Now sum over $n$ and $\frac 14$ of all children lose both parents.