biting

hello im wondering if anybody can offer any advice i have 2 girls one is 2 1/2 and the other is 16 months old, my younger daughter keeps biting my older daughter, up until now it has just been little nips that make my daughter cry, but today my younger daughter bit the older on so hard that it acctually broke the skin. up until now we have tried telling her off and lightly smacking her hand but nothing seems to make any difference, she bites for any reason sometimes it can be because  she wants something the other child has but sometimes it can be for no reason at all just because she can, im just not sure what else i can do to stop her, my health visitor has told me to just ignore it that she will grow out of it, but im getting worried about taking her back to stay and play group if shes going to start biting the other children, so far she only bitten her sister, any advice anybody could give would be much appreciated, thanx