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Yes. It is much more common to get a false negative then it is a false positive.

Pregnancy tests work by measuring the amount of a certain hormone in your urine. If you have not be pregnant for long enough then there won't be enough of that hormone present for it to recognize that you are in fact pregnant. Blood tests are much more accurate since they can tell from other hormones but it can only be preformed by a doctor.

All this info is in the pamphlet that comes with the pregnancy test. It's recommended that you use one on the day that you miss your period. If it's negative wait a few days and if your period shows up you are probably ok (this isn't 100%, you can get 'spotting' which seems like a period while pregnant) if not then you test again.

Why I ask:

My boyfriend came and visted me for my birthday...we ended up having sex but neither of us orgasmed... And I'm worried about precum.

Whats the possibility of me getting pregnant from that?

I'm extremely worried because I'm already a mom of a two year old that I can't really raise properly on my own.

We can't give you a percentage, only a doctor/gyno can do that.
And if you already have one child which you admit to not being able to raise properly, why not wait to have sex until you're older, more responsible, and won't be as stressed about getting pregnant again (by this I mean then you won't have to worry about having another child you "won't be able to raise properly")?

I would only add one thing to this: It's YOUR and HIS responsibility to make sure to stick to the rule.

A woman should not be expected to do all the birth control stuff, and neither hsould the man. You should both be in it together. If you can't do that, I would seriously reevaluate your relationship.

Besides, why are you wasting your time with a boyfriend when you have a child to raise? You should at least hold off on the lovie dovey stuff for awhile and really focus on becoming a "better" parent, since you say that you're having problems with it.

Yes, you can get a flase negative. The most effective way to take a pregnancy test is first thing in the morning, the first time you go to the bathroom, when the hormones in your urine is the most concentrated and haven't been diluted by everything you've been drinking during the day. Most all packages come with two sticks, so you can take one, and if it's not totally clear, or even if it is, you've got the second for confirmation.

Now, as far as your having sex... as others have said, if you can't take care of the child you already have, is it REALLY so hard to consider USING BIRTH CONTROL? I'm sorry, but it's a HUGE pet peeve of mine when girls freak out about getting pregnant, and then you find out they did nothing to prevent it. It's simple. Buy a condom. Get on the pill. Hell, do both.
If you can't handle your child, then you already know being pregnant is BAD. You also know how babies are made (or so I'd hope). So do the responsible thing and use freakin' protection or stop having sex. Set a good example for your child.