Let's consider the following situation:
You are a teacher in a school. A serious fire breaks out in your classroom during your class. All of the students are able to get out except for your daughter who is traumatized of fire and cannot move at the sight of it. You cannot take her with you, because you have broken arms and cannot improvise any other material to save her at this exact moment. Judging the situation, you determine determine that you have about 0.001% chance of saving her and a 99.999% chance that you will die together with her if you'd try to do so.
The question of course arises what is the most logical thing to do, should one save her or not?
Are there philosophers who have written about this sort of ethical questions, where the most favourable outcome is very improbable and very risky, but very favourable and 'ethically hard'? What are common arguments for and against the different opinions?
We could also imagine that the answer might depend on whether it is your daughter or just a random child. What are commonly seen opinions on this matter, and what are arguments for and against them?