### Probability of Destruction

[I picked this up off www.yesthetruthhurts.com]

I'm trying to answer the question: "What is the probability that a given weapon will destroy or immobilize a vehicle on one round of shooting?" As a newbie Sisters player, I've tried to run the numbers for an Exorcist, and I'm gonna run the numbers for other popular weapons as soon as I verify my numbers. I know that my formula doesn't account for multiple hits, but that only makes these estimates conservative.

Probability that an Exorcist destroys the given vehicle armor value in one salvo:
AV 10
Destroy: 57.51%
Immobilize: 69.59%

AV 11
Destroy: 48.13%
Immobilize: 60.25%

AV 12
Destroy: 36.75%
Immobilize: 48.13%

AV 13
Destroy: 22.95%
Immobilize: 32.44%

AV 14
Destroy: 6.26%
Immobilize: 12.2%

Any help appreciated,
Fifthman

P.S.: If you're a statistics kind of guy, here's the way I calculated the values:

Probability of a single missile dealing the desired damage (P1):
Easiest calculation, should be straightforward.
P1 = (P to hit)*( (P to penetrate) * (P of desired damage) + (P to glance) * (P of desired damage))

Probability of n missiles dealing the desired damage(Pn):
This is where the multiple hits issue comes in. The formula assumes, basically, that only one missile actually hits and the other n missiles miss.
Pn = sum from 1 to n of (1-P1)^(n-1)*(P1)

Probability of a salvo dealing the desired damage(Ps)
The probability that a number of missiles is fired is 1/6, and the probability that the given number of missiles is fired is Pn.
So, Ps = 1/6*P1 + 1/6*P2 + ... + 1/6+P6, or simplified to
Ps = 1/6* (sum from 1 to 6 of Pn)