This is a nicely openended question which will allow you to either stand out or look like an idiot.

I believe that they are less interested in the actual answer than in the chain of logic that leads you to your answers.

Declare an emergency. This gives you all kinds of help.

Like all airborne emergencies, above all, fly the airplane. This is most easily accomplished by having the F/O fly the plane on autopilot and deal with ATC while the Captain deals with the problem.

Many 121 operations manuals spell out in excrutiating detail what to do in the case of passenger illness.

First, don't even think about going back into the cabin to look at the passenger yourself. This is a security violation in that he may be faking to allow his terrorist friends to get into the cockpit when you come out.

Second, use all onboard medical help. This will usually start with a PA for medical professionals who may be onboard. Medical professionals certainly include doctors and nurses, but may also include med techs and veteranarians. 121 aircraft above a certain size must also carry an enhanced medical kit and an AED, which can be offered to the medical professional.

Third, use offboard assistance. Most 121 operators have a doctor either on staff or on call to assist in airborne medical emergencies. It may be useful for a F/A to come up to the cockpit to talk with the doctor on the ground. Dispatch can help with your decision making process and call ahead for the ambulance etc. Perhaps the airport that is 1:30 away has minimal medical facilities but an airport 1:40 away in a different direction is very close to a major heart center. These are not answers that you would be likely to know, but dispatch either knows or can find out much more quickly than you can.

This is all to aid you, the Captain, in deciding what to do with your aircraft and passengers. You may decide, based on what you hear, that the pax has an excellent chance of dying no matter what you do. You may decide that he has an excellent chance of living even if you go to the farther airport. In either of these cases the decision is easy. The only time a decision really exists is if a qualified medical person says that this person must get on the ground as soon as possible, and that any delay will kill him. This is when you must weigh the risks of a below minimums approach to the other passengers and crew against the life of this single person. That's why the Captain gets paid the big bucks.

You may take into consideration what type of below minimum conditions exist. Is it freezing rain with an out of limits crosswind to an airport in the mountains requiring a circling approach at night? Easy decision. Is it a calm day with dense fog to a CAT III ILS approach with an aircraft that is equipped with redundant autoland and auto rollout centerline tracking? This may be a harder decision.

I've made my decision, and it may or may not be the same one you would make, and there may not be a right answer.

In any case I believe that this question is not about what decision you make, but the thinking aloud about what you consider in arriving at your decision.

Joe