#prior-predictive

$y$ counts the successes in 5 independent trials with success probability $\theta$, and the prior is $P(\theta = \tfrac12) = 0.25$, $P(\theta = \tfrac16) = 0.5$, $P(\theta = \tfrac14) = 0.25$. Before any data are seen, what probability does the prior predictive distribution give to $y = 0$? Round to 3 decimals.