= Solution
Let $F_{A,B}$ denote the distribution function of the posterior <beta distribution>, with $A=a+s$ and $B=b+n-s$. This distribution is continuous with positive density on $(0,1)$. Its <equal-tailed credible interval> is
$$
\boxed{\left[F_{A,B}^{-1}(\alpha/2),\quad F_{A,B}^{-1}(1-\alpha/2)\right].}
$$
Compute the two quantiles by solving $\int_0^{\theta_L}\pi(\theta\mid x)d\theta=\alpha/2$ and $\int_{\theta_U}^1\pi(\theta\mid x)d\theta=\alpha/2$. Each excluded tail has mass $\alpha/2$, leaving posterior mass $1-\alpha$ between the endpoints.
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