a. Not worthless if time remains until its expiration? With time remaining until expiration, the possibility exists that the price of the underlying asset will change by a sufficient amount to put the option in the money. Investors who forecast that the price of the asset will in fact change by this much will see some value in the option.
b. Worthless at its expiration date? With no time remaining for the price of the underlying asset to change, there is no chance the option will ever be in the money. Since using an out-of-the-money option produces an immediate loss, no one will want it and its value will be zero.