#discrete-prior

$y$ counts the successes in 5 independent trials with success probability $\theta$. The prior is $P(\theta = \tfrac12) = 0.25$, $P(\theta = \tfrac16) = 0.5$ and $P(\theta = \tfrac14) = 0.25$. You observe $y = 2$. What is the posterior probability $P(\theta = \tfrac12 \mid y = 2)$? Round to 3 decimals.