Yashchenko I.V.

In the test, five answer options are given for each question. An excellent student answers all questions correctly. When a poor student manages to copy, he answers correctly, and otherwise, he answers randomly (that is, among the questions he did not copy, he answers $1 / 5$ correctly). In total, the poor student answered half of the questions correctly. What fraction of the answers did he manage to copy?
A poor student made mistakes in half of the questions. The number of questions he got wrong is equal to $4 / 5$ of the number of questions he answered randomly. This means he answered randomly on $1 / 2.5 / 4=5 / 8$ of the total number of questions. The answers to all the other questions he copied.

## Answer

$3 / 8$.

## Problem