Please assist me with the following scenario: Read this scenario, then address the short-answer questions that follow:

Lydia is involved in a dispute over an area rug she purchased from her neighbor, Tony. Tony's mother left him the rug in her will. Tony had no space in his home for it, so he offered it to Lydia. The two settled on what they thought was a fair price of $100.

A month later, an antiques hunter saw a picture of the rug and advised Tony that it was in fact a rare Persian rug worth at least $100,000. After learning of his mistake, Tony demanded that Lydia return the rug at once. Lydia refused, stating, "A deal is a deal."

1. Please help me understand what constitutes a mistake for purposes of contract law. Distinguish between a unilateral and bilateral mistake. If Tony argues that the rug should be returned because of a unilateral mistake, will he win his case?
2. Please help me understand what constitutes fraud for purposes of contract law. If Tony sues Lydia for fraud, will he win his case?
3. If Lydia is able to prove that neither party knew that the rug was a rare Persian rug, please explain whether or not if she can successfully defend against Tony's lawsuit? Please help me with an explanation.