You are looking at the proportion \(\pi\) of consumers who prefer MegaCola to its competitors. You use Jeffreys' prior hyperparameters, \(a_{0}=b_{0}=0.5\).

(a) You arrange blind tastings of MegaCola and and its competitors, and then ask the participants to indicate which one they preferred. After having tested 50, the feedback is that 41 of them prefer MegaCola. What are your posterior hyperparameters, and what is the probability distribution of \(\pi\) ?

(b) What is the probability that the proportion who prefer MegaCola exceeds \(75 \%\) ?