So I didn't actually play Stelaris before STNH, but I can see that there seems to be a random probability roll involved in each encounter. Even if I select the same options, I got 3 or 4 different outcomes in different play-throughs.

For example (very early fed game spoiler)
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Sending Archer to investigate in vulcan:
1. succeed
2. go to prison
3. die along with enterprise being destroyed (probably the worst outcome)

My question is, knowing that there is a random probability roll for what the outcome will be. Is there actually anything I can do to improve the odds on these rolls? i.e. will a more advanced ship or a more experienced leader, or a leader with a particular skill be able to get better odds of a good outcome? (in general, for any mission, not specifically for this one)

Thanks