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 $\displaystyle \frac{1}{4}*\frac{1}{4}*\frac{1}{4}=\frac{1}{64}$

(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?

Re: elementar probability question

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:

$\displaystyle P(X)+P(Y)=1$

$\displaystyle P(Y)=1-P(X)$

Now, compute $\displaystyle P(X)$ and then plug it into the above equation.

Re: elementar probability question

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

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

Re: elementar probability question