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.
Best Answer
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.