Probability of passing 90-question multiple choice exam with mostly guesses

[leopard]

I had a MCQ exam today. 90 Questions with 4 alternatives. I need help calculating my chances of passing (which should be really small).

I know 3 of my answers are correct. I gambled on the rest.

Also, please calculate the chance of passing, assuming that my guesses were a little more educated, so that the chance of hitting the correct answer was 1/3 instead of 1/4.

I need 36/90 correct to pass.

 

[CRGreathouse]

It's actually not too bad, since the passing grade is low. You need at least 33 out of 87 (since 3 are known to be correct), which is close to the 29 you'd expect guessing 1:3.

Pari tells me:

sum(k=0,87-33,2.^k*binomial(87,k))/3^87
0 ms.
0.2117180908186974588873520067

you have a 21.2% chance.