A RESOLUTION OF BERTRAND PARADOX

Bertrand's random-chord paradox purports to illustrate the inconsisten cy of the principle of indifference when applied to problems in which the number of possible cases is infinite. This paper shows that Bertra nd's original problem is vaguely posed, but demonstrates that clearly stated variations lead to different, but theoretically and empirically self-consistent solutions. The resolution of the paradox lies in appr eciating how different geometric entities, represented by uniformly di stributed random variables, give rise to respectively different nonuni form distributions of random chords, and hence to different probabilit ies. The principle of indifference appears consistently applicable to infinite sets provided that problems can be formulated unambiguously.