## Beta distribution posterior distribution

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?

Thanks