So I'm doing up the Captain's turn run sheet, and I thought I'd just pull a snippet from it.
Caitian 1 Distress Call 14 Colony World, Uprising, Prs-T, gain pp, avoid potential combat situation, 1 Easy DC, Resp: 3d6=11, Prs+Def Response, USS Polaris responds, 10, pass
To translate this:
Caitian Sector rolls a 1 on the Affiliate Sector chart, which is Distress Call event
The specific event is a 14, relating to a Colony World getting up in arms about something
This particular one requires a Prs-T (Presence Test), and offers Political Will as a reward
The Difficulty Roll is a 1, which is an Easy DC
The current system for generating a response roll is 3d6, which came out to 11.
I respond with the Amarkian sector, as the closest, and two ships are available to respond. Because it is an unplanned diplomatic mission, it is a Prs+Def roll. Each ship rolls, Polaris (2 Prs + 3 Def) + 2d6, and a Miranda (1 Prs + 2 Def) + 2d6. Polaris rolls an 11, the Miranda a 7, so Polaris is the only one able to respond.
It is an Easy DC, which for non-Explorers means a 6. Polaris rolls 2+2d6, gets a 10, so it passes the event.
Sol 17 Local Anomaly Research, Sci-T, 10 Hard DC, Unplanned, Resp: 3d6=7, Sci+Def Response, USS Stalwart+Miranda+Oberth Respond, Sci-T (Stalwart+Oberth), 12 pass
Sol Sector rolls a 17, for Local Anomaly Research
This is one of the ones where you basically wing the actual narrative event, so I don't roll a sub-type. These are always Sci-T (Science Test) and +rp
The Difficulty Roll is a 10, which is a Hard DC
The 3d6 came out to a 7, and because it is an unplanned Science mission, it is a Sci+Def Response.
Stalwart rolled a 15, the Mirandas a 9, 13, 7, and the Oberth an 11. So, four ships can respond, however, for the actual mission test, they'd just get underfoot without a proper doctrine to guide them (the extra Mirandas can tow the others to safety if something goes pear-shaped though).
the Sci-T then is taken by the stats of the two best Science vessels, the Oberth and the Constellation, giving us a 7+2d6 = 12, which passes the DC 11 of the hard test for non-Explorers.
Sarek 2 Mapping Mission 32 Discover Anomaly, Energy Field Resource, Sci-T, gain sr, 6 Med DC
USS Sarek rolls a 2, for Mapping Mission,
Rolls a 32 for sub-type, gets a Mapping Mission
Narratively, everyone is out on the Cardassian frontier, so I don't roll for other reinforcements from sector fleets
5YM Explorers don't roll to respond, they're always there
Difficulty roll is a 6, so Medium DC
Sarek is S8, so 8+2d6 = 13, passes the DC12 requirement.