kevin does not know the answer to two questions on a multiple choice exam.
the first question has five choices, the second question he does not know 
has six choices. what is the probability that he will get both questions 
wrong?

He will get the first question wrong 4 times out of 5, so
he will get the first question wrong 4/5ths of the time, which is to say,
the probability of getting the first question wrong is 4/5.

He will get the second question wrong 5 times out of 6, so
he will get the second question wrong 5/6ths of the time, which is to say,
the probability of getting the second question wrong is 5/6.

That means that 5/6th of the 4/5ths of the times he gets the first one wrong,
he will also get the second one wrong, too, so the probability that he gets
both wrong is 5/6th of 4/5, which is 4/5 times 5/6 or 20/30, or 2/3.

So 2/3rds of the time he will get both questions wrong. 

Edwin