Windshield wipers, air conditioning randomly going on and off

We just bought this car 3 days ago. We had it checked by a mechanic and everything checked out good. Well it was raining the other night and we had the windshield wipers on. Later on they would not shut off with me turning the switch on and off, then eventually shut off on their own. Then yesterday I was driving it and they just came on out of nowhere, and would not shut off. After a few minutes they went off on their own. Then today we were driving it and the air conditioning just shut off out of nowhere. We shut all the knobs off, then waited about 5 minutes and turned it back on and it was fine. We are worried this is going to cost a ton to fix, what does it sound like to you?