Final answer:
A check drawn on an out-of-town bank is the only option that can be accepted without risk, as third-party checks, postdated checks, and predated checks carry risks. The option (B) is correct.
Step-by-step explanation:
Out of the given options, the check that can be accepted without risk is a check drawn from an out-of-town bank.
A third-party check carries the risk of being fraudulent, as it is issued by someone other than the account holder.
A postdated check, which is dated for a future date, cannot be deposited or cashed until the specified date, making it less convenient for immediate payment.
A predated check, which is dated in the past, may be considered stale and may not be accepted by the bank.
An out-of-town bank check, on the other hand, is at lower risk as it is drawn on a bank located outside the immediate vicinity and may require additional verification. Therefore, option (B) is correct.