We study the behaviour of the Betfair betting market and the sterling/dollar exchange rate (futures price) during 24 June 2016, the night of the EU referendum. We investigate how the two markets responded to the announcement of the voting results. We employ a Bayesian updating methodology to update prior opinion about the likelihood of the final outcome of the vote. We then relate the voting model to the real time evolution of the market determined prices. We find that although both markets appear to be inefficient in absorbing the new information contained in vote outcomes, the betting market is apparently less inefficient than the FX market. The different rates of convergence to fundamental value between the two markets leads to highly profitable arbitrage opportunities.