Give an example of a situation in which you believe a type i error is more serious than a type ii error. give an example of a situation in which you believe a type ii error is more serious than a type i error. in each case, why do you think so?

Type I error is also known as a "false positive" and type II error as "false negative."

Example of Type I being more serious: Suppose you have a banking app that gives access to an authenticated user to transactional capability. In order to authenticate the user, a biometric test is done. If the biometric test makes a Type I error and falsely tests the user as positive (correct user), then an imposter who just got in, can transfer money away from the account. Otoh, if a true user gets rejected (type II error), it is a nuisance but not as serious as the loss of money.

Example of Type II being more serious: Suppose you have an app where a doctors can access patients' blood types. In an emergency, a doctor that fails to gain access due to a Type II error (false negative) won't be able to help the patient until they get an additional test done, which can be a serious delay. In this case a false negative  is more costly than the problem of letting in an impostor (false positive).