Explain Type I/II errors vs precision/recall

Within binary classification and hypothesis testing:

1. Provide definitions for Type I and Type II errors.
2. Explain how they correspond to false positives/false negatives and to precision/recall.
3. When is a Type I error more costly than a Type II error, and when is the reverse true? Give concrete examples.
4. Given a scenario, be able to recognize which mistake is Type I versus Type II (e.g., fraud detection, spam filtering, medical screening).

Overview: This question tests understanding of Type I and Type II errors in hypothesis testing and binary classification, their relationship to false positives and false negatives, and how those concepts connect to precision and recall in the Statistics & Math domain.