An expert gives +15%. Attributes give +5+10+15%. Battle Gnomes give +40%. Unicorns give 20% (and you can place 3 of them). Let's assume that artifacts with the skill stack, and the rest are calculated separately.
Chance = 1 - ((1-0.4) * (1-(0.15+0.05+0.1+0.15)) * (1-0.2) * (1-0.2) * (1-0.2)) = 1-0.6*0.55*0.8*0.8*0.8 = 0.83 = 83%

I took the time to do a quick test. On one hand, an expert for resistance (20%), gnomes (20%), and a squad of unicorns (20% each) - the calculated chance is 26.2%. On the other hand, an expert + artifacts (20 + 30%), battle gnomes (40%), and a squad of battle unicorns (20% each) - the chance is 12.3%. I ran more than 20 rounds - and here are the results: instead of 26.2%, it's 47.6%, and instead of 12.3%, it's 0.0%. I could have run 100 rounds, but the principle wouldn't change - the formula doesn't work (the game probably has a different one). And judging by the results, it's approximately this: %chance = 1 - (%hero resistance + %gnome + %unicorn (one! - does not depend on their number)). Then in the first case, the calculation is 1 - (20 + 20 + 20) = 40%, which is close to the actual result (47%), and in the second case, 1 - (50 + 40 + 20) = -10%, which corresponds to a 0% chance (in reality). I haven't checked the horn or rear yet, as both are present in the squad.