Maximum Likelihood Estimation given Uncertain Data

Question

during my lecture in uncertainty quantification i came across a problem where one has $2$ machines, that usually have a probability of producing a faulty part of $p1 = 10^{-4}$. Now we know for certain that Machine $1$ works properly, thus has this probability $p1$ of producing a faulty part. Machine $2$ on the other hand is expected to be damaged and has a possibility $p2$ of producing a faulty part. Each of the machines produce $50\%$ of the factories output. One is supposed to find the Maximum Likelihood Estimate for $p2$ given that $1000$ parts are examined, without knowing from which machine they came, and one faulty part is found. I dont know how to handle the uncertainty in the data? What is the Likelihood function, given that I dont know wheter the faulty part is from machine $1$ or $2$?