According to taransworld.com/chest the chances of pulling Mythic and Legendary troops are:

This means that you get 1 Mythic every 1 / 0.00096 = 1041 Gem Keys (on average)

Chances of not pulling a Mythic with a Gem Key are

1 - 0.00096 = 0.99904

Chances of not pulling a Mythic (k=0) with 1000 Gem Keys are

0.99904 ^ 1000 = 0.382716

This means that chances of pulling at least 1 Mythic (k>=1) are

1 - 0.382716 = 0.617284

Chances of pulling exactly 1 Mythic (k=1) are

where np = 1000 * 0.00096 = 0.96

P (k=1) = 0.96 * e ^ ( - 0.96) = 0.3675

P (k=2) = 0.96 * 0.96 * e ^ ( - 0.96) / 2! = 0.1764

P (k=2) = 0.96 * 0.96 * 0.96 * e ^ ( - 0.96) / 3! = 0.0565

P.S. Math rules.