The probability of indirect human fertilization?

Question

What is the probability of conception in situations when sperm isn't directly ejaculated into the woman's vagina, like:

1. The man's or the woman's hands come into contact with sperm, for example when removing a condom. (Perhaps after washing them,) the hands later touch vagina, for example during foreplay to another intercourse.
2. The man and the woman taking a bath together, the man ejaculates into the water.
3. The man ejaculates on the woman's body, perhaps on or around vagina but not inside. (In this case it could also make a difference whether the woman has shaved pubic hair or not.)
4. The man ejaculates during receiving oral sex, (perhaps the woman rinses her mouth), the couple kisses, the man performs oral sex to the woman.

In all these situations, it seems possible that a tiny amount of sperm is eventually transferred into vagina indirectly. And since just a single cell is enough to fertilize, it seems that there is non-zero probability of conceiving. How much care need to be taken to prevent conception in such situations? Does simply washing sperm away with water (+ soap perhaps) eliminate it?

_{If you think of similar situations that are similar, please don't hesitate to add them.}

Answer 1

I don't have answers to all of your questions, but here is one example of a highly unusual conception via the gastrointestinal tract: http://blogs.discovermagazine.com/discoblog/2010/02/01/ncbi-rofl-thats-one-miraculous-conception/

Answer 2

Very very very very small. Next to impossible, millions of sperm cells start the journey and only a very small fraction of the sperm produced make it as far as the egg if "inserted properly." The vagina is a very hostile environment - to prevent infection - and this means very few sperm make it far enough. We produce in the order of 200-300 million sperm and it estimated that less than 1000 make it, so that is a 0.000005 chance of each sperm cell making it far enough.

There is also a benefit to travelling in such large number (each sperm is less likely to be destroyed by dilution effects, one sperm cell vs the entire human reproductive tract stands no chance). The numbers I am giving may be a little out from the correct ones, it's a while since I did my undergraduate module in sperm biology... I'm sure more accurate numbers will be in this recommended reading

Further to this remember that not every attempt at fertilisation is successful even when doing it the right way, couples often try multiple times. If it takes 100 attempts to fertilise the egg just once the that is 1 in (100*200,000,000) sperm being successful.

Basically, if someone says they got pregnant sitting on a toilet seat that must have had sperm on it, or some other ridiculous claim, then simply don't believe them.