Of that 7/18, are you including the lowest ranked team that will inevitably end up being the opponents for City?
There are 22 teams left in the competition (including Liverpool), so 21 possible opponents we can draw.
Brighton / Swansea
Arsenal / Wimbledon
Chelsea / Villa
Man Utd / West Ham
Millwall / Leicester
Wolves / Spurs
Of the 21 teams still in the competition, 7 of them are non-PL teams: Preston, QPR, Stoke, and Sunderland are already through, plus Swansea, Wimbledon, and Millwall needing to win.The best case scenario
would be for 7 of the 15 teams in the draw to be non-PL (if all three of Swansea, Wimbledon, and Millwall win). That would give us a 46.7% chance of drawing a non-PL team, and 23.3% of a non/PL team at home
.Worst case scenario
would be for only 4 of the 15 teams in the draw to be non-PL (if all three of Swansea, Wimbledon, and Millwall lose). That would give us a 26.7% chance of drawing a non-PL team, and 13.3% chance of drawing a non-PL team at home
So regardless of results our chance of drawing a non-PL team will be somewhere between 26.7% and 46.7%
. And chances of a home tie against a non-PL team will be between 13.3% and 23.3%
Given these odds we should be pretty pleased with simply avoiding the top clubs (United, City, Chelsea, Spurs, Leicester, Arsenal). We'd have to be really lucky to draw a non-PL side, especially at home.