[Math] Chances in a multiple choice test

probability

Let's say there are 5 multiple choice questions, with the answers A, B or C. The chance that you get it correct by random guessing would be $\frac13$. I need at least 3 correct answers to pass the test. What would the chance be, with random guessing, that I pass the test?

A friend of mine told me that the chance was about $0.045$, using the binomcdf-function on the calculator, but this seems too small for me. Is this really the answer, or have we done it wrong?

Best Answer

The answer is wrong [edited]. Let's work it out together, see the comments on the question above.