An urn contain 5 balls, $\displaystyle \theta $ white and $\displaystyle 5 - \theta $ green. The experiment consists in grab 2 balls from the urn and register the pair $\displaystyle (x_1, x_2) $ , where $\displaystyle x_i = 1 $ we observe a white ball and $\displaystyle x_i = 0$ otherwise. What is the bayes estimator $\displaystyle \theta^* $ for $\displaystyle \theta $ considering the squared loss function? (i.e $\displaystyle l(\theta,\theta^*) = (\theta - \theta^*)^2 $ )

I can't figure out which posterior distribution I should use or even if I need to use one. I calculated my loss function considering all the possible values for $\displaystyle \theta $ and $$\displaystyle \theta^* $ but I can't calculate the risk function without the posterior function.

Can someone help me with it?

I can't find out what to do with the ordered pair, I just calculated the probability of each pair