relevant (Benford's law)

Have you seen this article I wrote? It is a non-drug-based depression-fighting story.

Have you signed up to see the therapist? It sucks that you have to wait a month, but it sounds like this has been going on a lot longer than a month and it is likely to continue for a lot longer than a month, so it's worth going even if you have to wait a month.

How long ago did her father die?

Generic Prozac costs me $4 a month. It has improved my mood greatly over the course of two months. I was afraid of side effects at first. Then, during one bad period, I remembered what exactly it was I was trying to cure and decided all the side effects that regularly come with and more are worth not going through that anymore. So is taking this stuff for the rest of my life.

SSRIs have varying levels of withdrawal symptoms (Prozac's is low, Paxil's high).One study on SSRIs shows that for many people they are not more effective than a placebo, but for the most depressed people they are extremely effective. If your girlfriend has sever chronic depression, there's a good chance the condition is genetic, and there's no very good way to fix that aside from medicine.

Dependence on a drug that is cheap, has few side effects, and can almost completely cure chronic depression is a very small price to pay for never feeling as worthless as depression can make you feel. I'm sure you can find many, many more such testimonials. If the side effects bother her, she can change drugs--there are a lot of alternatives.

My girlfriend suffers serious depression ... anorexia ... she considers herself very happy apart from the "depression periods"

The depression is very likely caused by some sort of dietary deficiency, and the depression periods are probably the periods when that deficiency is worst, so focus your attention on diet. If she isn't taking a multivitamin every day, fix that first. Then start keeping both a food log and a "daily mood" log. For the former, either write down everything eaten, or take a quick photo of it type up the log later using the photos. For the mood log, ask her to rate how she felt on a 1-5 scale and write it down at the end of each day. Then compare the two logs and look for patterns. Or publish the log and ask others to look for patterns.

"Imagine the human race gets wiped out. But you want to transmit the so far acquired knowledge to succeeding intelligent races (or aliens). How do you do?"

I got this question while reading a dystopia of a world after nuclear war.

I think Scenario 2 is wrong.

If you know, that one card is an ace, the probability that the second card is also an ace is 1/3, because there are two non aces and one ace remaining.

The tricky thing is, that it´s completely irrelevant, if the ace is of spades or of hearts. Remember, the question is if you hold both aces! Just distinguish between aces and non-aces..