How to calculate total chance from different simultaneous chances

Well, to add on to the topic, the general formula which I gave is to calculate something happening in exactly a certain amount of occurrences. (For example, the probability of rolling a 2 on a 6-sided die exactly 3 times out of 4.) You could also use this to calculate the probability of at least and at most events. For example, the probability of rolling a 2 on a 6-sided die at most 3 times out of 4. The at most includes rolling a two 0 times, 1 time, 2 times and 3 times. This could be done using the binomial probability distribution as well by using the formula for each number (in this cases there's 4; 0, 1, 2 and 3) and adding them together. Of course, this process can become rather tedious, which is why you'd probably want to use the Cumulative Distribution function mentioned earlier. I just find it interesting how they both work. (In case you were wondering, the probability of rolling a 2 at most 3 times in 4 rolls is 99.9%.)

Oh, also, the Cumulative Distribution only calculates "at most" situations. If you wanted to calculate an "at least" situation using it, you'd need to do "1 - at most value + P®"
So if you wanted to calculate the probability of rolling at 2 at least 3 times in 4 rolls, it'd be:
1 - .999 + .015 = .16%

I hope my explanations make sense. I feel like I tried to throw too much information into that one post... I'm a math major and can do stats all day.