I think I'm going to have to disappoint you. You're highly unlikely to solve it by chance.
You can do this with Binomial distribution. So if you plug the values in to this link: Binomial Distribution: Probability Calculator
0.25 - Chance of getting a question right
50 - Number of trial/questions
30 - Number of successes (questions you need to answer correctly to pass)
You want the P(X >= 30) value. Which is 1.64228554977441E-07. If you plug this in again:
The chance of her passing 1 or more times by chance in those 950 is approximately 0.000156 or 1 in 6410.