 Assuming no reason to favor one hypothesis over the other, the Bayesian approach would be to assign prior probabilities formula_31 and a uniform distribution to formula_18 under formula_33, and then to compute the posterior probability of formula_2 using Bayes' theorem,

After observing formula_36 boys out of formula_37 births, we can compute the posterior probability of each hypothesis using the probability mass function for a binomial variable,
where formula_39 is the Beta function.From these values, we find the posterior probability of formula_40, which strongly favors formula_2 over formula_3.The two approaches—the Bayesian and the frequentist—appear to be in conflict, and this is the "paradox".