Posterior probability of an obstacle from a noisy proximity sensor

A mobile robot uses a binary proximity sensor to decide whether a grid cell ahead is occupied by an obstacle. From a map prior, the probability that any given cell contains an obstacle is $P(O) = 0.05$. The sensor has a true-positive rate (sensitivity) of $P(D \mid O) = 0.95$ and a false-positive rate of $P(D \mid \lnot O) = 0.10$, where $D$ denotes 'sensor reports detection'. Given a single detection, what is the posterior probability $P(O \mid D)$ that the cell is actually occupied? Give your answer as a percentage.