Well, it depends on your luck, but it's less than a 2% chance (so < 1/50). From this old but rather extensive article (that I am wondering if I should update given newer games and updates to GO now...)
https://daily.pokecommunity.com/201...ame-shiny-and-perfect-pokemon/#perfectpokemon
Is that math correct? Calculated the odds below.
Same 5 IVs
Copies 5 of 6 IVs. Randomizes the imperfect stat with a 1/6 chance. Ranges from 0 to 31 from there. So:
(1/6) * (1/32) = 1/192, or 0.52%.
Different 5 IVs
Breaks this into three separate cases.
Case A: Picks Parent A's imperfect stat with a 1/6 chance. Rolls from 0 to 31, once again. Becomes a 1/2 chance on Parent B's imperfect stat.
(1/6) * (1/2) * (1/32) = 1/384
Case B: Mimics the above. Picks Parent B's imperfect stat. Flips a coin on Parent A's stat.
(1/6) * (1/2) * (1/32) = 1/384
Case C: Selects a stat both parents are perfect in with a 4/6 chance. Rolls the magic 31. Walks away with two perfects on the shaky stats with two separate 1/2 chances.
(4/6) * (1/2) * (1/2) * (1/32) = 4/768
Adds them together.
(1/384) + (1/384) + (4/768) = (8/768)
= 1/96, or 1.04%.
Or is there an error above?