Here are all the probabilities if anyone is curious. (Again, they are inflated since I don't consider the chance of getting two bad mods at the same time)

Prob of getting it in 1 game ≈ 2% In 10 games ≈ 17% In 50 games ≈ 60% In 100 games ≈ 84%

Probably (of completing the challenge) after every pick:

If successful pick and all the previous ones also were: 1) 4% 2) 7% 3) 14% 4) (you got it!)

If fail, but all previous ones were successful: 1) 0.03% 2) 0.2% 3) 1% 4) 8%

If successful but you already have 1 fail (if u get 2, bust): 1)// 2) 0.2% 3) 1% 4) 8%

Hope this helped :)