I don't remember much of my high school math, but try this:
On any roll of a d20, you have 5% chance of a particular number being rolled. That means you have a 95% chance of some other number. If you want to know the odds of a number being rolled, simply figure the odds of something else being rolled instead.
Example:
4 rolls of a d20, 95% chance to roll something other than a "1".
.95*.95*.95*.95=.8145
You have an 81.45% chance of NOT rolling a "1", therefore you have an 18.55% chance of rolling at least one "1".
Note, the general rule of thumb gets you pretty close - you have a 5% chance of rolling a "1" each time, so just multiply 5% times 4 rolls = 20% chance. It's not perfectly accurate, so for more detail use the method above.
Also, this is just a statistical average - you could theoretically roll a d20 a thousand times and never roll a "1" - the odds are almost nil, but it is possible (that's why we say someone is rolling "hot" or "cold" at times).
Second note, the method above only works to determine the chance of rolling at least (but possibly more than) one "1" - I don't remember the formula for figuring the chances for only one roll of "1" out of four rolls. If anyone knows the formula, I'd love to see it.
Hope this helps.
