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Doing this for mathhammer....

I'm looking to figure out the chance for a complex firing unit to inflict a specific number of wounds on simple target unit.
complex firing unit; ie a unit with multiple types of ranged weapons
simple target unit; ie same T & Sv throughout the unit

example: a unit of guardsmen fire 12 shots from lasguns and 2 shots from meltaguns against a unit of X space marines
the 12 shots have a ~11.9% chance of causing 2 wounds [2 successes / 12 trials / ~5.7% chance of success per trial ]
the 2 melta shots have a ~17.4% chance of causing 2 wounds [2 successes / 2 trials / ~41.7% chance of success per trial ]
but what I'm really looking for is the likelihood of the combination of the shots cause 2 wounds (and 2 wounds only) from the combined fire of the unit

I'm at a loss with how to approach this with my amateur probabilities, and was hoping that someone may be able to give me a leg up.

Edit: title

Well, first of all, everything is way easier in fractions.

so you have 1/2 x 1/3 x 1/3

so, 1 in every 18 shots will cause a wound

then you have melta shots

1/2 x 5/6

so 5 in every 12 shots will hit

The odds are LOOOOOOOOOOOOOOOOOONG to kill 2 marines... I will calculate it shortly

(edit) Okay.. so the odds of killing 2 guys with 2 rolls from the melta guns is 25/144

then for killing 2 guys with 12 rolls from lasguns is around 1.5% I think... sorry, I lost count.

If you want to know the way I did this..pm me, cause I'm too lazy to explain it right now if no one is interested

and I have no idea how you would combine the two calculations... sorry

It doesn't matter anyway, it's just about luck u guise.

Orkeosaurus wrote:It doesn't matter anyway, it's just about luck u guise.

QFT.

Superstition is way easier than stats. Just about as effective too.

If you call them "miss"le launchers they'll miss.

You have to call them hitle launchers.

And never forget to wear your unwashed pair of lucky underwear.

Plot out the binomial distribution of each set, then look at the combinations that get you to two casualties, and then combine the odds of each of those.

So for the 12 lasgun shots you have the following;

0 kills 0.50
1 kill 0.36
2 kills 0.12
3 kills 0.02

For the meltagun shots you have the following;

0 kills 0.34
1 kill 0.49
2 kills 0.17
3 kills 0.00

To get two kills you can have two lasgun kills and no meltagun kills, one of each or two meltagun kills and no lasgun kills.

So you have

2 lasgun * 0 meltagun = 0.12 * 0.34 = 0.04

+

1 lasgun * 1 meltagun = 0.36 * 0.49 = 0.18

+

0 lasgun * 2 meltagun = 0.50 * 0.17 = 0.09

For a total probability of scoring two kills of 31%

Thanks sebster, that's exactly what I was looking for.