RARE - At least 1 rare or better in each pack.
EPIC - Average of 1 every 5 packs.
LEGENDARY - Average of 1 every 20 packs.
There is also some kind of algorithm giving you a guaranteed epic/legendary if you don't get one at x-amount of packs. You will also get a guaranteed legendary from 10 first packs of each expansion. Here is source. https://hearthstone.gamepedia.com/Card_pack_statistics
RARE - At least 1 rare or better in each pack.
EPIC - Average of 1 every 5 packs.
LEGENDARY - Average of 1 every 20 packs.
There is also some kind of algorithm giving you a guaranteed epic/legendary if you don't get one at x-amount of packs. You will also get a guaranteed legendary from 10 first packs of each expansion. Here is source. https://hearthstone.gamepedia.com/Card_pack_statistics
Also note that there is varying amounts of rares/epics/legendaries beetween expansions, so it maybe easier or harder to get the one you want.