But as a doctor, probably you will have to choose non-randomly, if you want to stand by your utilitarian viewpoint, since killing different people might have different probabilities of success.
Assuming the lest convenient possible world hypothesis, you can’t make your own life easier by assuming each one’s sacrifice is as likely to go well.
So in the end you will have to assume that one patients sacrifice will be the “best”, and will have to decide if you kill them, thus reverting to the original problem.
But as a doctor, probably you will have to choose non-randomly, if you want to stand by your utilitarian viewpoint, since killing different people might have different probabilities of success. Assuming the lest convenient possible world hypothesis, you can’t make your own life easier by assuming each one’s sacrifice is as likely to go well. So in the end you will have to assume that one patients sacrifice will be the “best”, and will have to decide if you kill them, thus reverting to the original problem.