Finding the probability of selecting a correct answer I encountered this very elementary problem  as I was practicing probability.

In a multiple-choice test, each question offers a choice of 5 answers,
  only one of which is correct. The probability that a student knows the
  correct answer is 5/8. If he does not know which answer is correct, he
  selects one of the 5 answers at random. Find the probability that he
  selects the correct answer to a question.

I'm having difficulties understanding where they received the denominator(8) from, shouldn't it be 1/5 ? Further what is the best way to tack this problem?
Thank you.
 A: Sometimes, he does know the answer, so the options don't matter.  He just ticks the right answer.  That happens 62.5% of the time.  The other 3/8 of the time, he has no idea, and the only thing he can do is pick one at random.  Sometimes, he gets it right this way.
A: So $\frac58$ of the time the student gets the question right by knowing it.  The other $\frac38$ of the time the student guesses, and so $\frac15$ of $\frac38$ of the time the student gets the question right by guessing.
A: I would say $5/8 + (1/5 * 3/8) = 5/8 + 0.6 / 8 = 5.6 / 8$. The "best" way to "tack" this problem would be to write it down on a piece of paper and tack it to some corkboard.  I think you meant attack this problem.  The denominator $8$ is because there is a 5/8th chance he knows the answer to each question so it is a good denominator to "start" with.  For my answer, I just kept the subexpression of ($1/5 * 3/8$) in terms of 8ths simply by dividing the numerator $3$ by the $5$ in 1/5th.
One interesting thing is that if $70$% was the lowest passing grade on this test, this person would (on average) pass by guessing at the answers he didn't think he knew at the $5/8$th confidence level.  If he just left those blank (and thus got them wrong), he would (on average) get $62.5$% which would be a failing grade.  However by guessing, it would bring that up to $70$% which is a passing grade.
A: 
The probability that a student knows the correct answer is 5/8.

In 5 of 8 cases, the student ticks the right answer (1/1 is correct). In the other 3/8 he takes one by random, where the propability is 1/5.
p=(5/8)(1/1) + (3/8)(1/5)= 7/10= 0.7
