Dorothy mistakenly accused Fred's son, Steven, of negligently burning down

Dorothy mistakenly accused Fred's son, Steven, of negligently burning down Dorothy's barn. Fred believed that his son was guilty of the wrong and that he, Fred, was personally liable for the damage, because Steven was only fifteen years old. Upon demand made by Dorothy, Fred paid Dorothy $25,000 for the damage to Dorothy's barn. After making this payment, Fred learned that his son had not caused the burning of Dorothy's barn and was in no way responsible for its burning. Fred then sued Dorothy to recover the $25,000 that he had paid her. Will he be successful?