If there are 50 screws should be tested, the worker A has a prior experience that 60% of the screws are bad. Now, the result is that 15 screws are good, 35 are bad. Assume $p$ is the probability of a screw which is tested as good,and we known that $0.3 \le p \le 0.5$.
My question is how could I derive a prior distribution of $p$ which is in accordance with the experience of worker A? Because I do not know what kind of distribution of $p$ is, could I make it any distribution with $E(p)=0.4$? Is the distribution unique?
Thank you very much!