Hi all, can anyone help with this question?

The proportion \theta of defective items in a large shipment is unknown. However, experience suggests that a Beta(2,200) prior is appropriate. Suppose that 100 items are selected at random from the shipment and that three are found to be
defective. What is the posterior distribution of \theta?

Suppose that another statistician, having observed the three defectives, said that
his posterior distribution for \theta was a beta distribution with mean 4/102 and variance 0.0003658. What prior distribution had that statistician used?