Assuming your 12k gems are spent on gem keys, I calculate a 83% chance at getting at least 1 mythic

If they are VIP keys, I calculate a 96% chance of at least 1 mythic.

For the curious:
2k glory keys = 18.1%
250 gem keys = 22.2%
1200 gem keys = 70% or 266 vip keys = 93%
4500 seals = 10.6% (assuming you still get guardians, otherwise this goes up to 20.1%)

Chance of mythic in 1 key = 0.001 (1 in 1000)
Chance of non-mythic in 1 key = 1 - 0.001 = 0.999
Chance of all non-mythic in n keys = 0.999^n
Chance at least 1 mythic in n keys = 1 - 0.999^n

If guardians are present, you get 112 non-guardians, so n = 112
1 - 0.999^112 = 1 - 0.8939 = 0.1061 = 10.6%

If guardians are not present, n = 225
1 - 0.999^225 = 1 - 0.7984 = 0.2016 = 20.2%

One example I like about probability: Imagine flipping a coin and getting heads 26 times in a row. The odds are just staggeringly small. But if everyone in the US tried it one, there is a 99.3% chance someone would get it.

I think the Law of large numbers is most prominently visible when it comes to all kinds of lotteries. There is a really tiny chance you’ll get the jackpot (probably 1 in dozens of millions) yet someone gets it.

I’d suggest waiting until the next big data dump. We’ve had a few new details about mythics and such, but nothing about events after July 24. I’d wager either tonight or next week they will add the August and September event schedule to the game data. At that point it would be worth starting fresh again.