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If T is any subset of \({\mathbb{Z}}[X]\) then the probability \(P_ d(T)\) for a polynomial F of degree not exceeding d to lie in T is defined as the limit (when H tends to infinity) of the ratio \[ \#\{F\quad in\quad T: \deg (F)\leq d,\quad H(F)\leq H\} / \#\{F: \deg (F)\leq d,\quad H(F)\leq H\} \] and the probability for a polynomial to lie in T is defined as lim \(P_ d(T)\) for d tending to infinity (if all the limits in question exist). The author shows that the probability for a polynomial to have no fixed divisors equals \(\prod (1-p^{-p})\) \((=0.72199...)\), the product taken over all primes.