Hi all, can anyone help with this question?

The proportion 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 ?

Suppose that another statistician, having observed the three defectives, said that

his posterior distribution for was a beta distribution with mean 4/102 and variance 0.0003658. What prior distribution had that statistician used?

Thanks