(Problem 4.14 in the Dutch book.) Here is a paranoid algorithm to compute the maximum of a set A of n real numbers.
Algorithm ParanoidMaximum(A)
(a) If $|A| = 1$, then return the unique element $x \in A$.
(b) Otherwise, pick a random element $x \in A$.
i. $x' := \text{ParanoidMaximum}(A \setminus \{x\})$.
ii. If $x \le x'$ then return $x'$.
iii. Otherwise, we suspect that $x$ is the maximum, but to be absolutely sure, we compare $x$ with all other elements in A. Finally, return $x$.
Analyze the expected running time of this algorithm.