I am not sure such utilitarian math is the true solution, attempts to put a number on the value of human life seem all silly. I would rather say that the failure of a robotic mission costs an amount X, while the failure of a human mission intuitively has infinite price.
Conversely setting human life to infinity cost quickly breaks down with the trolley problem. Any problem where groups a or b are going to die then whatever group is bigger lives, even if it doesn't make sense, such as group b is all very old and group a is very young but slightly smaller.
Trolley problems are an exercise in utilitarianism and maybe generally consequentialism. If those are your views, then you can probably put a number on it. Other views are available, however. (See sibling mentioning deontology.)
To be fair, it's not really a breakdown of the trolley problem. It's the point of the trolley problem. Setting the value of a human life to infinity basically gives you deontology, in that both outcomes are approximately equally bad, and thus your choosing to get involved at all is unethical.
