The difference between 'result' and 'outcome'

Result is something tangible and something immediate, while outcome is intermediary, leading to far reaching impact.
If you're asking the people who you've submitted the application, it wouldn't make a lot of sense to ask for the outcome, because the entire future is not under their control. It would make more sense to ask for the result, which could be that you passed or failed, and/or if whether you are accepted or rejected.

Deontic [social sense] 'may' asking for permission doesn't sound natural mixed here with the stative verb 'know', Jane. It's sounds awfully epistemic, level of certainty meaning, but that's obviously not the sense you intend.

Is it possible for me to know ... ?

???May you tell me ... ?

Jane "finding" or "verdict" might apply though not quite collo

http://thesaurus.com/browse/outcome?s=t

"Upshot" might go

http://thesaurus.com/browse/result?s=t

Hi Skar,
if two persons fought, can I ask them the outcome?

If you mean boxing or MMA, the conventional word that would be used is 'result.' But in a casual conversation over a beer with a friend or a colleague, you may hear, in some instances where someone will interchange the word 'result' with 'outcome.' In sports, 'result' and 'outcome' in most cases conveys the same linguistic meaning. An example of a case where these two words ceases to be synonymous is when discussing sports injuries.

Thanks a lot for your explanation.