What is the Equation for Calculating Probability in a Specific Range?

[dave2118]

Hello

I'm trying to remember back to my high school / college days and have no idea where to start.

Basically, I'm trying to find probability in numbers for a specific range. I'd like to figure out an equation so I can plug it into software. Here are my sample values below:

0,36
100,55
200,66
300,80
400,97
700,99
800,99.3

So this line will basically never hit 1. I can't for the life of me figure out what to search for on google for this, I remember doing something easy back in school, but it's been a good 20 years, and actually need to use it.

Any direction would be great.

Dave

 

[gb7nash]

What's the exact problem? I can't really tell what your question is. What does it mean to "find probability in numbers for a specific range"? What are those sample values you listed? What exactly are you trying to find the probability of? etc..

 

[dave2118]

There's a system called the Elo Rating System (http://en.wikipedia.org/wiki/Elo_rating_system). I'm trying to figure out the probability of Player A vs Player B. I played around in excel using Ln which is sort of what I'm looking for based off of a table similar to http://www.ascotti.org/programming/chess/elo.htm

I was hoping to simplify it the best I could.

 

[spamiam]

If you really want there to be a horizontal asymptote at y=1, log won't do the trick since it's unbounded. Maybe something more along the lines of
$$f(x) = \frac{x+1}{x+2} = 1 - \frac{1}{x+2}$$
would work, since it does have a horizontal asymptote.

 

[CellCoree]

Hello Dave,

It seems like you are trying to find the probability for a specific range of values. In probability, we use the equation P(A) = n(A)/n(S) to calculate the probability of an event A occurring, where n(A) is the number of outcomes that satisfy event A and n(S) is the total number of possible outcomes.

In your case, you have a set of values and you want to find the probability for a specific range. To do this, you will need to first define your events and outcomes. For example, if you want to find the probability of getting a value between 100 and 200, then your event A would be "getting a value between 100 and 200" and n(A) would be the number of values in your set that fall within that range. Similarly, n(S) would be the total number of values in your set.

Once you have defined your events and outcomes, you can use the above equation to calculate the probability. In your case, since the values are not evenly distributed, you will need to use a weighted probability formula. This can be done by dividing n(A) by the sum of all the values in your set (n(S)).

I hope this helps. If you need further assistance, I recommend consulting a statistics textbook or seeking help from a math or statistics tutor. Best of luck!