Maybe we can simplify the problem even further, and just consider two swings. This is a 16 second fight, meaning the third JBB results in mob death.
Ticks happen at times 0, 6, 12
One swing happens at t=0. If it procs, it does 44 + 24 * 3 or 116 damage
The second swing happens at t=8. If there was no prior proc, it does 44 + 24 * 1 or 68 damage. If there was a prior proc, it does 44 damage.
1) If both swings proc, the total damage is 116 + 44, or 160 damage.
2) If just the first swing procs, the total damage is 116.
3) If just the second swing procs, the total damage is 68.
4) If neither swing procs, the total damage is 0.
Case 1 happens with probability 1/12 * 1/12
Case 2 happens with probability 1/12 * 11/12
Case 3 happens with probability 11/12 * 1/12
Case 4 happens with probability 11/12 * 11/12
The total expected damage is the sum of the expected damage of each of the four cases, weighted by the probability
160 * 1/144 + 116 * 11/144 + 68 * 11/144 + 0 * 121/144
The total expected damage is 15.1 in this scenario
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