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I'm not too good at math, but I consider myself competent on a basic level. However, when it comes to advanced statistics, I think I could use a lot of help! This is a problem, because Mathhammer is ALL about stats.

I'm trying to calculate which has a better chance to wreck a Flyer in one shot, the Quad or the Icarus. Please correct my math if it's wrong. (I'm expecting I made a mistake someplace.)
I play BS4, so I'm going with that value. I'm also shooting at AV12.

Let's start with the Icarus, since it's easier to calculate.
First off, if my Psyker somehow isn't TL.
Chance to Hit * Penetration S9 vs. AV12 * Missed Jink * AP2 Explodes
4/6*3/6*4/6*2/6 = .0741 = 7.41%
When he is TL, the To Hit changes to 8/9, which makes the whole thing = .0988 = 9.88%

So far so good?

Now, the Quadgun. With four shots, it's possible to either wreck or explode a Flyer, making the calculation much more involved. I'll start with the Explodes result
Chance to Hit, TL * Penetration S7 vs. AV12 * Missed Jink * AP4 Explodes
8/9*1/6*4/6*1/6 = .0164 = 1.64%
However, there's four dice, so we multiply by 4 to get 6.58% chance to explode

Put that number aside, to add in later
Now I need to figure out the chances of removing three hull points in one go. I'll have to cube each value, because I need to make three of the hit/glancepen/missed jink
Chance to Hit, TL * S7 vs. AV12 * Missed Jink
[(8/9)^3]*[(2/6)^3]*[(4/6)^3] = 0.0077 = 0.77%

Add that to the above to get 7.74%


Now, some things I'm concerned about in this analysis:
I didn't calculate how getting two Immobilised results would wreck a vehicle, instead of the normal three. This would raise the chances of the Quad gun, although not very much.
I'm also quite suspicious that I did the math wrong, since I would expect it to be significantly more likely to wreck the Raven, rather than Explode it. My numbers say the opposite, though.

Please, someone confirm/fix my math!

Quadgun is wrong.

You can't just take the probability of one shot result and multiply it by the number shots. Once you have the relevant probability for one shot, you need to use a binomial distribution to calculate your probability to destroy by successful explodes or knocking off hull points successfully or whatever .

Also, you want to run the numbers for at least one explodes, or at least three hull points, or at least two immobilized for your destroyed events. Not exactly one or exactly three etc....

Finally, you want to subtract some of the probabilities that get double counted.

Hope it helps. If you are still having trouble I can pm you my flier stats excel sheet when I get off work.

Probability for multiple events taken together gets a bit messy.