[Alt-text] Spongebob and Patrick work out their strategy with a utility based analysis.
We tend to assume that the means accomplish the ends, but that's not necessarily the case. The trolley problem never looks at where the trolley is going, just how it gets there. But if the way we want to get there doesn't actually go to the destination we want, then it's not a solution. Hope this helps. =D
edit: trolley is spelled with an e
There are definitely goals that are statistically improbable that are beyond are current means to navigate consistently, like getting rich through lottery tickets, but they don't violate physics. We do have to take into account what we are able to influence, practically speaking, with our actions.
I bring up physics because we live in a physics-based universe as opposed to a moral universe. So our analysis of our course of actions must take that physical reality into account when pursuing a subjective moral outcome. If we lived in a moral universe, like D&D, we would only need to ask do the ends justify the means. Acting to achieve a goal in a such a universe would, in theory, always be a matter of acting in a way that was consistent with the end goal. But that's not the universe we live in.