Rape, statistics, criteria and probability

Since this has come up again and again in discussions about Schrödinger's rapist, I thought I'd put together something about statistics and probabilities, which is something most people don't really understand.
Not that I was a mathematician or something, so, it's a layperson's explication for laypeople.
If I make factual errors please correct me.
The latest example of this is in The Crommunist's excellent post on Racism and Schrödinger's Rapist.
Here are the facts people can mostly agree on (I'm too lazy to link the sources right now. Ask me and I'll do so):

• Between 1 in 6 and 1 in 4 women are raped during their lifetime.
• They are alsmost exclusively raped by men (98%)
• Between 1 in 15 and 1 in 20 men are rapists.
• Most women are raped by someone they know, only about 3% of women are raped by a stranger.

Those are pretty scary statistics, but they look a lot better once you turn them around:

• 75-86% of women are never raped
• 93-95% of men are not rapists
• The stranger on the street is safer than the acquaintance who's giving you a ride home.

Therefore, people argue, it is unfair to contemplate the idea that a random stranger you meet at night in a dark area might be a rapist. The chances of being raped there and then are very small. It's also unfair to make this decision due to the sex of the person. After all, they also all have 2 eyes and I don't treat 2-eyed people as potential rapists.

There are several problems with this which I'll try to show.

1) Probability never hits the individual with 3%. Any risk/chance is calculated on a large number of data. When the actual event happens, there's only 1 or 0: you don't win the lottery 1:480.000.000. You either win it, or you don't. While it is a fact that the chances of winning the lottery are extremely small, people do indeed win the lottery.
Smaller example: When you throw a dice, the chance of rolling a 6 is 1 in 6. And the average number you roll is 3.5. The moment you throw it, the chances break down. The number is cast and you'll never roll a 3.5.

2) 3% isn't a small number. 5% isn't a small number. If you get that much interest, or have to pay it, you notice 3% quickly.
Walk along highstreet and count the women. Statiscally, number 6, 12, 18, 24 have been raped by somebody they know, number 30 by a stranger.
Count the men. Number 20 is a rapist (statistically. Don't do this with a group of people you know, it might drive you nuts). He has raped an average 6 times.
How many times can you repeat that exercise until you reach your office/the supermarket/etc?

3) Those numbers are people. The example above should have demonstrated that we're talking indeed about a lot of people. Above, we just assigned the value rape survivor / rapist by statistics. You have no clue who they actually are. Probably the first man you met was the rapist, maybe none in the first 20 was a rapist, but 16, 17 and 18 in the second set of 20. As long as there are no additional criteria/information, you cannot tell. And you ignore the peril at your own risk.

4) There are necessary conditions, sufficient conditions and red herrings.
The fact that all rapists have (more or less) two eyes is not in any way corelated with rape. It's a logical conclusion of them being humans. As a criterium to distinguish between potential rapists and harmless people, it's absolutely useless, since I cannot eliminate anybody by that.
If I want to be aware of poisonous snakes and be able to tell them from harmless snakes, "no legs" is a useless criterium.
Other criteria make more sense. The fact that most rapists are men is more usefull*. Now, as people rightly pointed out, viewing all men as potential rapists doesn't make much sense either, not any more than all grey snakes when, although all poisonous snakes were grey, only 5% of grey snakes are poisonous. But, honestly, which snake would you be more wary of if you found it on your terrace, the grey one or the green one?
So we add more criteria. Is he trying to isolate me? Is he getting uncomfortably close in a lone area? Does he follow me into confined spaces? Now, none of those criteria necessarily mean rapist. There are perfectly non-rapy reasons for doing so, maybe he doesn't notice that he's isolating me, or he really just wants to be helpfull and make sure that I get home safely. Maybe he's just heading home. Maybe he just confused the doors because he's a bit drunk himself.
Fact is, although those behaviours might be harmless, they are also the exact same behaviours a rapist would show. Those are, so to speak, necessary conditions for a rapist. But they are not sufficient conditions. The sufficient condition is the rape. That's when you cast the die and if it comes down as a six you're raped. So, is it reasonable to wait until that moment, or should you avoid rolling the die?
Maybe this grey, 2m long snake with the checkered pattern is completely harmless and just mimicking the looks of the poisonous 2m checkered grey snake, but since you can't tell until you're attacked, is it reasonable to be carefull with all 2m checkered grey snakes?


*What did I just say about numbers? 4 in 1000 women are raped by women. But I'm lacking data about how many women are raped by strange women. I don't think the numbers are the same, but just for the sake of the argument, let's use the same numbers as for men:
15% strangers: 6 in 10.000 women are raped by a strange woman.
Each rapist rapes about 4 new victims (they rape 6 times, the difference is due to women being victimized more than once), so 1 in 1000 women you meet is a rapist.

5) Schrödinger's anybody
In our daily lives, we engage in a lot of Schrödingers'.
-If you drive a car, you engage in Schrödinger's reckless driver. You monitor those around you for potential mistakes and outright violations. If you have right of way and a car approaches, you assess the situation, you watch it the other driver slows down to yield or not.
Does that mean you accuse the other driver unfairly of being an incompetent idiot who can't drive?

-If you engage in casual sex, you find it reasonable to use a condom for protection. Does that mean that you unfairly accuse the other person of having an STD?

-If you shield the panel while at the ATM, do you unfairly accuse the person behind you of being a criminal?

-If you don't open your door for a stranger while alone at home, are you unfairly accusing the other person of being a burglar?

If your answer is no to all the above, why are you upset at women being wary around strange men in a dark car-park.