Odds of Two 1% Encounters at the Same Time?

Question

I'm using Cheryl in Eterna Forest in Platinum to hunt for a shiny Budew, and while here, I ran into a (regular) Dustox and Beautifly at the same time. In Platinum, those are both 1% encounters, and it hasn't really come up nor is my search yielding results that help, so I was just curious about the chances of a double encounter like that, where both are 1% odds. I don't think it's that uncommon, since 1% isn't particularly rare, I'm just curious what this would look like in a 1/??? sort of ratio. Gives me a little extra to look forward to during a boring hunt! Thank y'all

Answer 1

Since there are two Pokemon that spawn, and Beautifly and Dustox both appear 1% of the time in each slot, simple probability can be used to calculate the odds of both of them spawning together.

1% (Beautifly spawn rate) x 1% (Dustox spawn rate) x 2P2 (since it can be either Beautifly Dustox or Dustox Beautifly)
= 1% x 1% x 2
= 0.02% (1/5000)

That's actually a bit rarer than the odds of finding a shiny in the forest (2/8192 = 0.0244%, unless idk how shiny odds work in the platinum forest), so uhhhh yeah congrats I guess?

Hope I helped!

Comments

If all shiny chances are independent from each other, then the average number of shinies you get per encounter should be 2/8192. The chance of getting any non-zero amount of shinies should be a tiny bit less than that.