What are the odds of a L8E skip?

[ComputerGuy365]

What are the odds of this?

This means all centers done, first 3 cross edges, and the last yau edge. What is the odds of the rest of the edges already being solved?

 

[xyzzy]

1/15!! = 1/2027025 ~ 0.00005%

 

[ComputerGuy365]

1/15!! = 1/2027025 ~ 0.00005%

Care to explain why?

 

[One Wheel]

In place or paired? By my (probably wrong) figures chances are (I'm presuming this is 4x4):
1/15 for the first edge (15 places on the cube for the second half of the first edge to be)
1/13 for the second edge
.
.
.
1/2,027,025 for all edges paired, plus a 1/2 chance of OLL parity.

I've never gotten that. I've gotten 3 or maybe 4 edges paired, possibly even 5, but definetly not more than that.

 

[xyzzy]

In place or paired? By my (probably wrong) figures chances are (I'm presuming this is 4x4):
1/15 for the first edge (15 places on the cube for the second half of the first edge to be)
1/13 for the second edge
.
.
.
1/2,027,025 for all edges paired, plus a 1/2 chance of OLL parity.

This explanation is correct. An alternative calculation is that there are 8! 2^8 ways to permute the wings such that they're paired, and 16! permutations of the wings in total, so you have (8! 2^8) / 16! = 16!!/16! = 1/15!! as the probability of skipping edge pairing. (Note: !! means the double factorial.)

(The probability of skipping edge pairing and solving the edges fully is just 1/16!.)