# Looking for conjugate priors for a Binomial likelihood

The likelihood function is a Binomial one -- say $$k$$ failures in $$n$$ trails given the probability of failure is $$p$$.

The $$p$$ is a function of two independent r.v. $$x$$ and $$y$$: $$p=a-bx+cy$$ where $$a$$, $$b$$ and $$c$$ are known constants in the range of $$[0,1]$$, $$[0, \infty)$$ and $$[0, \infty)$$ respectively. $$x$$ and $$y$$ are both in the range of $$[0,1]$$.

Now the problem is, once I observe some data $$k$$ anf $$n$$, I want to do bayesian inference on the $$x$$ and $$y$$. I am thinking to use conjugage but cannot find good priors for them... even good approximation is ok.

Also I see there is the problem that the range of $$p$$ could be out of $$[0,1]$$, is there anyway we somehow choose the priors that can change/rescale the range of $$x$$ and $$y$$ to make sure $$p \in [0,1]$$?

I am wondering how you can make sure that $$0\leq p\leq 1$$ with the given conditions. We can easily see that $$a-bx+cy$$ can range from $$-\infty$$ to $$+\infty$$.