I am one that would throw the entire basket of strawberries away, but you do not have to. First, discard the strawberries with mold. Next, rinse off the ones that look fine and do a taste test. If they seem to taste good, then they should be okay to eat.
Strawberries are individual entities. Mold can easily travel from one to the other, but one is usually the culprit (as it was probably plucked before the others). Check your other strawberries carefully and give them a nice wash, and you should be fine.
Keep in mind that mold grows UNDER the surface first, before it shows, thus especially the strawberries on the moldy side, even if they look okay, can already contain the basic decay that makes eating moldy fruit dangerous (and even poisonous). If you have particular mold allergies you should be extra careful.