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?
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.