What type of statistical error occurred when a failing student is passed by an examiner

The type of statistical error that occurs when a failing student is passed by an examiner is a Type II error (also called a "false negative" error).

Type II error occurs when a hypothesis test fails to reject a false null hypothesis. In this case, the null hypothesis (the student is competent or should pass) is wrongly accepted, when in reality, the student should have failed.
In contrast:

Type I error would occur if a competent student is wrongly failed (false positive).