Necessary, because if this were not true — if half or more people who commit embezzlement/bribery do NOT repeat that crime — then the premise that asserts “more crimes → greater chance of being caught” would no longer provide support. In order for that author to think that premise helps prove the conclusion, he must believe that most people who commit embezzlement/bribery will commit that crime again.

Not necessary, because although we know that people who repeatedly commit crimes like embezzlement or bribery WITHOUT BEING CAUGHT tend to become more confident, that doesn’t imply that most people who commit embezzlement/bribery are confident. Most people who commit embezzlement/bribery might be caught the first time and not become more confident. It’s just the ones who are NOT CAUGHT that tend to become more confident.

Not necessary, because the author never compares embezzlement/bribery to other kinds of crimes.

Not necessary, because although the author believes that people who repeatedly commit embezzlement/bribery are more likely to be caught, that doesn’t require those people to become more careless over time. Perhaps the reason they’re more likely to be caught is just that police are able to gather more and more evidence, regardless of the criminals’ level of care. The criminal can be just as careful, but still leave more and more evidence over time.

Not necessary, because even if (E) were not true, and there are some people who are caught the first time, the argument applies to people who are NOT caught the first time.