I am trying to create a formula for the % chance of having Y number of dice hit a number 8, 9 or 10 out of X possible. For example the chance of having 7 dice out of 10 dice be one of the 3 numbers.
In other words I need a formula where you can insert X(number of 10 sided dice rolled) and Y(minimum number of die you want to hit 8, 9 or 10 (In other words 3/10)), and get the percent chance of this happening.
I've spent all night coming up with different formulae that describe the problem but none of them have worked... Please help.
Cheers.
P.S. The full extent of the problem is that whenever one of the dice hits 10, another die is added to the value X but I imagine that would make the formula extremely complicated but if you have a reasonable way to add it to the equation then please go ahead.
As I understand your question, you have $x$ number of dice (of specific shape&probability) and you define a specific result to be a "success" or a "failure" (in your example, rolling an 8,9, or 10 on a d10). You roll all $x$ dice and count how many successes you had total, and you are interested in the probability of having either exactly or at least $y$ successes.
This is given by the Binomial Distribution. It says that having exactly $r$ successes out of $n$ trials with a specific probability $p$ for success in each trial occurs with probability $$P(X=r)=\binom{n}{r}p^r(1-p)^{n-r}$$
If you are interested instead in at least $r$ successes instead, then add up each case of exactly more to get $$P(X\geq r) = \sum\limits_{i=r}^n \binom{n}{i}p^i(1-p)^{n-i}$$
Wolfram Alpha's calculations for your specific choice of numbers below.
Your calculator said "not solvable"? That suggests to me that you probably used an incorrect syntax somewhere. If using a graphing calculator in the Ti-83 family, to calculate the probability of exactly $r$ successes out of $n$ trials with probability of success $p$, you would type
To calculate probability of at most $r$ successes out of $n$ trials with probability of success $p$, you would type
To calculate probability of at least $r$ successes out of $n$ trials with probability of success $p$, you would type
To do so without built in commands, then for the case of at least $r$ successes out of ... you would type something like this:
The specific syntax for summation is:
To find more information on how to use specific functions of your graphing calculator, I recommend reading the manual which should either have come with it at time of purchase, or is available online on the manufacturer's website.