Three More From a Fresh Prior
A new free-throw shooter has an unknown success probability $p$. Before any data, your prior for $p$ is Beta(2, 3). Given $p$, each shot is an independent Bernoulli($p$) trial. You watch her take 5 shots and she makes 4. What is the posterior predictive probability that she makes all of her next 3 shots? Give your answer as a reduced fraction.
Related problems & prerequisites
Worth solving first
- The Two Coins 4.0/10
Source: Original problem written for AxiomIQ (standard Beta-Binomial posterior predictive calculation). Statement written for AxiomIQ.