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The probability for quantum creation of an inflationary universe with a pairof black holes in higher derivative theories has been studied. Considering agravitational action which includes quadratic ($\alpha R^{2}$) and/or cubicterm ($\beta R^{3}$) in scalar curvature in addition to a cosmological constant($\Lambda$) in semiclassical approximation with Hartle-Hawking boundarycondition, the probability has been evaluated. The action of the instantonresponsible for creating such a universe, with spatial section with$S^{1}XS^{2}$ topology, is found to be less than that with a spatial $S^{3}$topology, unless $\alpha < - \frac{1}{8 \Lambda}$ in $R^{2}$-theory. In the$R^{3}$ theory, however, there exists a set of solutions without a cosmologicalconstant when $\beta R^{2} = 1$ and $\alpha = - 3 \sqrt{\beta}$ which admitprimordial black holes (PBH) pair in an inflationary universe scenario. We notefurther that when $\beta R^{2} \neq 1$, one gets PBH pairs in the two cases :(i) with $\alpha$ and $\Lambda$ both positive and (ii) with $\Lambda$ positiveand $\alpha$ negative satisfying a constraint $6 | \alpha | \Lambda > 1$.However, the relative probability for creation of an inflationary universe witha pair of black holes in the $R^{3}$-theory suppresses when $\alpha > - 2\sqrt{\beta} $ or $|\alpha| < 2 \sqrt{\beta} $. However, if the aboveconstraints are relaxed one derives interesting results leading to a universewith PBH in $R^{3}$-theory without cosmological constant. PACS No(s). :04.20.Jb, 04.60.+n, 98.80.HwComment: 15 pages, No figures. accepted in Int. J. Mod. Phys. D (2001

PROBABILITY FOR PRIMORDIAL BLACK HOLES IN HIGHER DERIVATIVE THEORIES