elementar probability question

I need help with this question:

A student is writing a multiple choice quiz consisting of three questions, each having four choices and one correct answer each.

(a)what is the chance that the student will get a perfect score by guessing?

I think this should be

(b) what is the change that the student will get at least one question correct by guessing

I'm not sure how to tackle this part. How do I calculate at least one right answer?

a) I agree.

b) It is certain that the student will either get no questions correct (event X), or will get at least 1 correct (event Y), so we may state:





Now, compute and then plug it into the above equation.

so P(X)= 3/4 * 3/4 * 3/4 = 27/64

and therefore P(Y)=1-(27/64) = 37/64

Yes, good work! :)