Sure. In terms of odds, Bayes' theorem says (posterior odds) = (prior odds) * (likelihood ratio) The prior odds are 1/999, so we need to show that the likeli

Sure. In terms of odds, Bayes' theorem says (posterior odds) = (prior odds) * (likelihood ratio) The prior odds are 1/999, so we need to show that the likelihood ratio is 2^10. The likelihood ratio is the probability of seeing 10 heads from a double-headed coin divided by the probability of seeing 10 heads from a fair coin, which is 1/((1/2)^10) or 2^10.