A warehouse receives crates of components from exactly two suppliers, and one crate has arrived with its label torn off.
Before opening it, the manager knows only the shipping mix:
The manager pulls 5 components at random from the unlabelled crate and grades them. 3 are premium and 2 are standard. Within a crate, each component's grade is independent of the others.
Treating "the crate came from X" and "the crate came from Y" as the two competing hypotheses, update the manager's belief with this evidence.
What is the posterior probability that the crate came from Supplier Y?
Round your answer to 3 decimal places.