Can we trust AI if we don't know how it works?

We're at an unprecedented point in human history where artificially intelligent machines could soon be making decisions that affect many aspects of our lives. But what if we don't know how they reached their decisions? Imagine being refused health insurance - but when you ask why, the company simply blames its risk assessment algorithm. Or if you apply for a mortgage and are refused, but the bank can't tell you exactly why. Or more seriously, if the police start arresting people on suspicion of planning a crime solely based on a predictive model informed by a data-crunching supercomputer. These are some of the scenarios the tech industry is worrying about as artificial intelligence (AI) marches inexorably onwards, infiltrating more and more aspects of our lives.