  Pandora's Box is a central problem in decision making under uncertainty that
can model various real life scenarios. In this problem we are given $n$ boxes,
each with a fixed opening cost, and an unknown value drawn from a known
distribution, only revealed if we pay the opening cost. Our goal is to find a
strategy for opening boxes to minimize the sum of the value selected and the
opening cost paid.
  In this work we revisit Pandora's Box when the value distributions are
correlated, first studied in Chawla et al. (arXiv:1911.01632). We show that the
optimal algorithm for the independent case, given by Weitzman's rule, directly
works for the correlated case. In fact, our algorithm results in significantly
improved approximation guarantees compared to the previous work, while also
being substantially simpler. We finally show how to implement the rule given
only sample access to the correlated distribution of values. Specifically, we
find that a number of samples that is polynomial in the number of boxes is
sufficient for the algorithm to work.
