# Probability of an unprepared student passes a quiz, 3 of 7 must be correct with 4 possible answers each?

A quiz consists of 7 multiple choice questions, each with 4 possible answers. To pass the quiz, it is you must get at least 3 questions correct. An unprepared student can do nothing except guess answers at random. What is the probability that the student passes?

I'm thinking you use the distributive property which gives you ${7 \choose 3} (0.25)^3 (0.75)^4$ but I'm not sure where to go from here.

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If by (3 7) you mean ${7 \choose 3}$, the ways to select $3$ items from $7$, you have calculated the chance to get exactly $3$ correct, not the chance to get at least $3$.
@JeremyQuick: I would also calculate $4,5,6,$ and $7$ and add. Alternately, I would calculate $0,1,$ and $2$ and subtract from $1$ as there are fewer cases. – Ross Millikan Oct 9 '12 at 17:34