Answer by Devendra Desale.

It depends on the question as well as on the domain for which we are trying to solve the question.

In medical testing, false negatives may provide a falsely reassuring message to patients and physicians that disease is absent, when it is actually present. This sometimes leads to inappropriate or inadequate treatment of both the patient and their disease. So, it is desired to have too many false positive.

For spam filtering, a false positive occurs when spam filtering or spam blocking techniques wrongly classify a legitimate email message as spam and, as a result, interferes with its delivery. While most anti-spam tactics can block or filter a high percentage of unwanted emails, doing so without creating significant false-positive results is a much more demanding task. So, we prefer too many false negatives over many false positives.

• False positive
  Improperly reporting the presence of a condition when it’s not in reality. Example: HIV positive test when the patient is actually HIV negative
• False negative
  Improperly reporting the absence of a condition when in reality it’s the case. Example: not detecting a disease when the patient has this disease.

When false positives are more important than false negatives:
– In a non-contagious disease, where treatment delay doesn’t have any long-term consequences but the treatment itself is grueling
– HIV test: psychological impact
When false negatives are more important than false positives:
– If early treatment is important for good outcomes
– In quality control: a defective item passes through the cracks!
– Software testing: a test to catch a virus has failed
SOURCE

Look at similar question on ROC curve and the youtube video link share there: https://mockinterview.co/index.php/question/explain-how-a-roc-curve-works/ — it has some intuitive explanation of when to prioritize what — TL;Dr is that it depends on business context.