= Solution
An <equal-tailed credible interval> for a continuous <posterior distribution> has probability $\alpha/2$ below its lower endpoint and $\alpha/2$ above its upper endpoint. If $F$ is the posterior <cumulative distribution function>, the endpoints are $F^{-1}(\alpha/2)$ and $F^{-1}(1-\alpha/2)$.
A <highest posterior density interval> is a <credible interval> consisting of points of highest <posterior density>: every included point has density at least as high as every excluded point, apart from null-set and boundary choices. It is a posterior <highest density region> when that region is an interval. For a continuous unimodal density with two interior endpoints, their densities agree. A mode at a support boundary can instead force one endpoint to that boundary; a multimodal posterior can have a disconnected highest-density region rather than one interval. Equal tails and highest density need not give the same interval.
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