Monday, August 8, 2011

Probability 101

Something with a little meat on it today. I was going to revisit a bit talked about here with the two weapon/multi attack problem. The problem is there is a lot of points and areas that one could excel at over the other in some thinking on the problem. Too much for that today so I'll go over a bit of probability as a primer to that.

First bit about probability. Probability in the mathmatic terms refers to, the instances in which an event happens out of all possible events. The "all possible events" is commonly called the sample space, it's not so much all possible events as so much as the ones you can get to with your experiement. So from this figuring a simple one is rolling a 1 on a six sided die. There is only one instance of 1 out of a total sample space of 6, so the result for rolling a 1 is  1/6. It doesn't even have to be a singular number, it can be something more complex like rolling higher than a 4 on a six sided dice. The number of instances this happens is two, them being 5 and 6, causing the probability of rolling above a 4 to be 2/6 or 1/3 through reduction. Simple until you start looking into multi variable problems but I won't beat your head over those too much.

Another thing that I should prime on is the "average" number or mean which is the "center" of most bell curves(a term that isn't exactly needed for this right now). For all purposes at the moment this will mathematically work for us, it's determined by adding the highest and lowest number together and dividing by two producing the theoretical mean, it's useful for guessing where most of the dice will be rolling.  There is another form of averaging which is also called a mean it is taken through gathering data points, you take every item add them all together and then divide by how many items there were. This is how they get average life expectancy, age, and other thigns. It's not perfect but it's one of the useable estimations, there are others out there.

Such as mode. Mode is the instance in the sample space that is the most likely to occur.  Five people aged 20 , three 23 year olds, and one creepy 50 year old show up to an event. The mean of this is 24 and the theoretical mean is 35, the mean derived by the actual numbers is clearly better here but still not exactly close enough. The single 50 year old is generally known as an outlier in these, or an odd event that generally doesn't happen but is taken into account because it did. Because of this the mean has shifted far further than it should have. So by looking at the mode we'll see that there were five 20 year olds which is more than the three 23 year old and the one 50 year old. You now have what is your most likely event if that was what you were actually looking for. It's useful for what is called unequal distributions. Where the most likely instances of occurrence are not actually clustered. I'll make a poorly labeled graph to try and get the point across. The green curve if I could actually draw this right under some average measurements would appear to have a "peak" in the middle like the red curve when it plainly isn't true. Mode can shed some light on just how much it is skewed if you look at it with the average next to it.

The last bit of probability I want to talk about is the median. The median is not something I use that often but probably should. Effectively you take all data or sample space and sort it then find the exact middle based on number of items and say that's the middle. Half of everything you can see falls above this point, and half of everything falls bellow it. It's like the illegitimate offspring of the mean and mode but I prefer some actual number useage when it comes to my disecting of these problems.

Well hopefully this wasn't too horribly long, incomprehensible, or boring but in the future this may save me some trouble. It's funny as people find probability to be some mystic strange thing when compared to other math. While I just find it to be the only one I can come to understand. Might as well finish this with a question for you guys as it's becoming a trend. What things that seem hard to other people seem to naturally click with you?


  1. computers, I just seem to make them work in the face of others struggling with something for hours.