Bayesian Posterior for a Biased Die

A biased die has an unknown probability $\theta = P(\text{roll} = 6)$. You place a $\text{Beta}(2, 8)$ prior on $\theta$ -- reflecting a prior belief that sixes are rare (prior mean $= 0.2$). You roll the die $n = 20$ times and observe $k = 6$ sixes. 1. Derive the posterior distribution of $\theta$ given the data. 2. Compute $P(\theta > 0.30 \mid \text{data})$ and express it in terms of the regularized incomplete beta function $I_x(a, b)$. No numeric integration required.