KnifeMissile

Well, since you already have 10 questions "in the bag," the real question becomes the chance that you get at least 14 questions out of the 30 questions left. If we let _nC_k be the choose function, then there are ₃₀C₁₄ ways of getting exactly 14 right answers. If there's a 1/5 chance of getting an individual question right, the chances of getting exactly 14 right answers out of 30 are (1/5)¹⁴×(4/5)^30-14. To address the question of the chances of "or more," we must sum over the chances of the individual numbers. So, the chances of getting 14 or more questions right is _{i∈[14,30]}∑(₃₀C_i×(1/5)ⁱ(4/5)^30-i).

Of course, this is a pretty wordy formula and my impromptu summation notation probably didn't help readability all that much, but there you have it. You can probably write a script to get a numeric answer, easily enough...