Full automation using Artificial Intelligence (AI) predictions may not be optimal if humans have information not available to the AI (contextual information). We study human-AI collaboration using an information experiment with professional radiologists. Results show that providing (i) AI predictions does not improve performance on average, whereas (ii) contextual information does. Radiologists do not realize the gains from AI assistance because of errors in belief updating – they underweight AI predictions and treat their own information and AI predictions as statistically independent. Unless these mistakes can be corrected, the optimal human-AI collaboration design delegates cases either to humans or to AI, but rarely to AI assisted humans.