Example. Existence of a false accept is not selected-output failure [ftip-00E7]

Suppose two candidates are produced: candidate 1 is invalid and falsely accepted, while candidate 2 is valid and rejected by a separate score tie-break. Then \(\bigcup _iF_i\) occurs, but a selection rule that always chooses candidate 2 outputs a valid response. Thus an existence probability and a selected-output probability coincide only after the selection law is specified.