I have the same question, which is the sole reason I'm scrolling the forums right now. The newspaper says 11 per year, so as long as we can believe that info, its not random numbers of eggs but I'd guess its random spawn rates. Not sure if any of this data is at all helpful for ya on trying to sus out the probability but heres where I am at as a fellow mid-event starter:
2026 Finds - 14 (Egg Hunt 2-8 of April)
13:34:50 - 02/04/26 Yellow Easter Egg
22:24:49 - 02/04/26 Green Easter Egg
22:46:57 - 02/04/26 Yellow Easter Egg
22:47:25 - 02/04/26 Green Easter Egg
00:31:50 - 03/04/26 Red Easter Egg
13:53:29 - 03/04/26 Brown Easter Egg
04:29:01 - 05/04/26 White Easter Egg
12:59:09 - 05/04/26 Red Easter Egg
15:46:20 - 06/04/26 Yellow Easter Egg
16:38:20 - 06/04/26 White Easter Egg
22:32:45 - 06/04/26 Yellow Easter Egg
22:33:35 - 06/04/26 Blue Easter Egg
12:31:32 - 07/04/26 Red Easter Egg
12:40:05 - 07/04/26 Green Easter Egg
2025 Finds - 7 (Egg Hunt 17-23 of April)
03:30:39 - 19/04/25 You created your account
15:06:43 - 19/04/25 Green Easter Egg
16:56:41 - 19/04/25 Yellow Easter Egg
01:32:40 - 20/04/25 Red Easter Egg
01:05:01 - 21/04/25 Black Easter Egg
01:09:02 - 21/04/25 White Easter Egg
12:25:43 - 21/04/25 Green Easter Egg
23:53:28 - 21/04/25 Red Easter Egg
edited to add additional egg finds