MY husband is on house arrest does his probation officer have right to randonly search the house?

Yes, a probation officer typically has the right to conduct random searches of a residence if the individual is on probation or house arrest, as part of the conditions of their supervision. This authority is usually outlined in the terms of the probation agreement. However, the specific rules can vary by jurisdiction, so it's important to review the conditions set by the court or consult with a legal professional for guidance.