User blog comment:Tenebraeh/Resummon Gate/@comment-26947994-20160722033327/@comment-26947994-20160722060245

First, we find the probability that Azurai is not summoned (assume 25/26). Then for every summon, there is a 25/26 chance that he is NOT summoned, so there is a (25/26)^12 chance (about 62.5%) that over the 12 summons, he will NOT summon a single Azurai. Because you either summon an Azurai or you don't (no in between),

(Azurai is not summoned) +  (Azurai is summoned) = 100%.

Switching around variables, we have:

(Azurai is summoned) = 100% - (Azurai is not summoned),

so the probability that you summon at least one Azurai is 100% - 62.5% = 37.5%.

What I meant about the 5* and 7* thing was that Azurai has to be summoned as a 7*. The rates for pulling a 7* straight out of the summon gate (no evolution) is most likely to be lower than the rates to pull a 5*. Therefore, the rates for Azurai will be lower than the rest of the units because the rest of the units can be summoned at 5* or 6* (higher rates) while Azurai can only be summoned as a 7* (lower rate).