A Probability Anecdote

The use of probability ideas to solve apparently unrelated problems is a fascinating subject. Paul Erd(?)s is a noted exponent of such uses and has proved many results in analysis, number theory and combinatorics in this way. A famous example is Serge Bernstein's brilliant proof of Weierstrass's theorem on approximation of continuous functions by polynomials. Another example is the nondifferentiability of Brownian sample functions (of which a quick proof is due to