Past exam of the year 1 of the computer science course of the University of Oxford / 2014 / Discrete mathematics, continuous mathematics and probability / 7 / b / iv

If the selected coin has bias $p$, the other two biases sum to $3/2-p$. A uniform choice between those two coins therefore has conditional head probability $3/4-p/2$. Average over the posterior distribution, using the previous posterior predictive probability:The observation makes a high-bias coin more likely to have been removed from the remaining pair.