I wasn't expecting to have to write this one, but it appears I do :D
The most common misconception about probability is SO common it has a name - The Gambler's Fallacy. It's the mistaken belief that past independent events affect future ones.
To explain it with an example: suppose you toss a coin five times and it comes up heads five times. Assuming its an unbiased coin, what is the probability of the next coin being a head?
The amusing thing here is the gambler's fallacy manifests itself in two ways here, depending on the person concerned: some people say 'it's bound to be another head', and some people say 'tails are due'. Both are wrong - this is, in fact, entirely irrational behaviour.
What if I'd tossed the coin in private, and it had come up heads five times in a row, and I hadn't told you, and asked you to say whether heads or tails was more likely? The odds are still evens, 50%, call it what you will. The coin doesn't have any memory of its previous tosses.
It does rear its head in more subtle ways: let's go back to the previous post. The chance of not getting a 3+ when rolling 3 dice (note, it doesn't matter if you roll three dice together or one after the other, or the same dice three times) is 3.7%. The chance of succeeding is therefore 96.3%.
What if you throw three dice one after the other, and fail on the first dice?
I'm pretty sure some people's (conscious or not) thought process would be "that's alright, Mike said I have a 96% chance of success on three dice, I'm still good!".
You're not. You now have to make 3+ on one of two dice. So the probability of failing to do so is the chance of rolling a 1 or 2 twice, which is 1/3 * 1/3, or 11%. Your chance of success has dropped to 89%.