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I currently trying to figure out what the chance of a meltagun at equal to or less then 6" getting a vehicle destroyed result. How do I do the 2d6 for the penetration roll?

The probability of getting exactly x on 2d6 is:

(6-|x-7|)/36

Since I have no mathematics background, but love theory hammer and math hammer I need more tools...

use a dice chart like this one

http://www.nextshooter.com/trueodds

Count up the number of the results that penetrate the vehices armor, divide that by total results (there are 36). That decimal you get is the percentage of times that you'll pen. An AP 1 weapon destroys a vehicle on a 4+. That is half. So multiply the first result you got on your calculator by 0.5. That percentage is the chance that a 'hit' well destroy a tank.

Now, this is quick and dirty. I'm sure a probability or statistics major is going to waltz in here and tell you how oversimplified and silly my answer was. Thats ok, They have the expertise to go about it a different way.

You can use this method to calculate glancing hits too. You could generate a chart that broke down percentages of what happens based on one dice throw, after you've created something like that, you will have a good understanding of how effective your shots are.

So to find out the chance to damage a landraider with a meltagun at 6" or less would be probability of getting 6-12 added together?

ie:
((6-|(6)-7|)/36)+((6-|(7)-7|)/36)+((6-|(8)-7|)/36)+((6-|(9)-7|)/36)+((6-|(10)-7|)/36)+((6-|(11)-7|)/36)+((6-|(12)-7|)/36)

Yes, though you are including glancing and penetrating there.

If you want the probability of getting a destroyed result, you would find:

(probability of getting 7, 8, 9, 10, 11, or 12)*1/2 + (probability of getting 6)*1/6

because meltas are ap1

I don' t know the probablity of destroying a vehicle with a metla gun, but I can tell you on average how many vehicles a melta gun will destroy. The difference is that you can set probability to any number you want (although you'll never get to 100%) and then figure out how many shot it will take to get that probability. The average gives you an expectation value. You'll need the stat guys to give you a better explination of that, but here are the numbers for BS 4 melta guns.

BS 4 melta gun fireing at AV10 => .33 kills
BS 4 melta gun fireing at AV11 => .31 kills
BS 4 melta gun fireing at AV12 => .29 kills
BS 4 melta gun fireing at AV13 => .25 kills
BS 4 melta gun fireing at AV10 => .21 kills

This considers results of destroyed and explodes as "kills", does not take into consideration the possibility of destroying a vehicle due to cumulative weapon destroyed an immobalized results, and does take into account the affects of AP 1. If the vehicle is in cover, divide these numbers by 2.

The formula above is a start, but I figure if that makes sense to you, you probably wouldn't be here asking for help.

Lets say you want to find the expected chance of a destroyed result for melta gun versus AR14 when it is whithin extra pen dice range.

First, what is required to glance and pen? 6 to glance and 7 or better to pen.

As nrs02004 has shown, probability of a single result on 2d6 is (6-|x-7|)/36. So for glance it is easy:

(6-|6-7|)/36 = (6-1)/36 = 5/36

So probability of a destroyed result via a glance would be (assuming BS4).
2/3 hit * 5/36 glance * 1/6 AP1 destroyed result = 5/324

Now we need to find the probability for a destroyed result via a pen. Since a result of 7 or greater will get you a pen, we need to find the probability of getting a 7-12. When you use that formula, you find 7=6/36; 8=5/36, 9=4/36, 10=3/36, 11=2/36 and 12=1/36. Add em up and you get 21/36.

So probability of a destroyed result via a pen would be (assuming BS4).
2/3 hit * 21/36 pen * 1/2 AP1 destroyed result = 63/324

Now add them up and you get 68/324, which reduces to 17/81. So a 20.99% chance of destroying AR14 vehicle with the extra pen dice.

Easy way for most people to calculate this for different ARs would be to use a spreadsheet (although there are even easier ways if you know what you are doing).

HTH

For those who don't understand the |x-7| part:

Any expression within the two vertical lines is called the "absolute value". What this means, simply, is that if the number is negative, you make it postive.

For example, with |x-7|:
x=11 is 11-7=4, which stays 4
x=1 is 1-7= -6, which becomes 6

The more you know!

That helps a lot. Thanks.

Is there away to do the absolute values in microsoft excel?

not sure, but I would guess:
abs()

This tactica has values for various weapons against tanks for guardsmen (BS3). It uses a more inclusive definition for effective damage.

http://www.dakkadakka.com/wiki/en/Tank_Hunting_for_the_Imperial_Guard