Question: Scores on a freshman mathematics exam are described by the pdf \[f(x)=6x(1-x),\] \[0\le x\le 1,\] where X represents the proportion of questions a student answers correctly. Any score X below 0.40 is a failing mark.

(a) What is the probability that a student fails?

(b) If six students take the exam, what is the probability that exactly two fail?