That probability depends on every transaction using 4 rounds of mixing (not likely), as well as assembling a 100% complete transaction, which isn't necessary for an attacker to draw hasty conclusions.
yep, but if you do the calculation using just one round it's still a huge number of days.
As for complete transactions, I agree that's not included....but I was answering your 'gun in the crowd' point, which has a probabilty of near 1, which is astronomically different to the proabilities we're talking about here.
It would be nice to know what are the average or most comonly used mixing rounds in a darksend, and calculate probability based on that. Or, even better, calculate attacker probability based on the minimum allowable amount of mixing, to establish a "worst case scenario" or baseline probability.
ok i'll do it then
with 15% of the network compromised and just one round of darksend per transaction the probability is 3.32526E-17 or .0000000000000000332526
mutiply by 1,000,000 for transactions per day (which is a really big number of darksend transactions, by the way):
.0000000000332526
and divide into 1 for number of days to get a complete transaction:
30072836410