# 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.

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.

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.

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.

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