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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?

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    Greetings, welcome to philosophy.se. Without giving us some sort of theory or framework that you want us to work from, this is really just asking for our opinions ... – virmaior May 12 '15 at 6:27
  • @virmaior I can't seem to find a place in which SE community this question belongs to. Can you help me identify how I can add some sort of theory or framework in this question? – Swindles May 12 '15 at 6:38
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    I guess I would split my answer into two parts. There is as far as I am aware no place on the SE system for questions that are purely opinion-based, so as written, there's nowhere for it. To make it fit here, you would need to explain what sort of ethical framework we're dealing with; you can find a short list of these here: en.wikipedia.org/wiki/Normative_ethics so we can answer in accordance with those restrictions. For instance, role ethics cares that we are talking daughter vs. random stranger. But then the %s make it look like you want this to be a numeric calculation. – virmaior May 12 '15 at 6:41
  • @virmaior Thank you for your replies. After further reading, I think i can conclude that there could be no right answer here since the origin of the question is based on morality and the answer I am soliciting is subjective. I 'll just let this question get closed – Swindles May 12 '15 at 7:20
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    Hello Swindles, welcome here. I have edited your question to ask for commonly seen opinions in established philosophies, which would be on topic (I'm also voting to reopen). I hope I did not change the original meaning of your question too much - if I did, feel free to roll back the edit though. – Keelan May 12 '15 at 7:30
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The presence of quantified probabilities in your question indicates to me that you are asking if this problem can (or cannot) be converted in the computation of a utility function. In the end, you point out a possible exception to this approach: the presence of a singularity: whether the girl is the person's daughter, considered as a unique individual, not as the member of a genus.

An ethical dillema can stay unresolved in both cases. A utility function is just one of many possible candidates, and even if you come to decide for a particular one, it can easily be too hard to compute, or even impossible (undecidable). A singularity can move you towards some kind of response, but this is not the same as moral judgement, in that it doesn't relieve you of the responsability to decide (to judge) what is your standing, considering what happened, even if you had no part in the actual event.

Philosophical theories of moral judgement begin by assuming that genuine moral dillemas stand on their own feet as phenomena, in that they are not reducible to what can be coded as law, or attributed to chance. Will these theories necessarilly lead us to metaphysical considerations? Well, that's another question.

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