Let's assume we have prior distribution beta with parameters 2,50. Let's just say it's prior knowledge of sign up rates for our product.
Then we have two binomial models A and B, which both samples from the same prior. The population is 100 and the target for A is 2, while the target for B is 20.
Now, if you check posterior distribution in your preferred tool, you can see model B has much better rates. The distribution curve of model B is shifted much more to the right of the X-axis than for model A. Does this mean there are much bigger chances for 20 people to sign up for our product than 2??? This seems very unlogical, considering our prior distribution. How should I interpret this? Thank you.