  In the present work, we quantize a closed Friedmann-Robertson-Walker model in
the presence of a positive cosmological constant and radiation. It gives rise
to a Wheeler-DeWitt equation for the scale factor which has the form of a
Schr\"{o}dinger equation for a potential with a barrier. We solve it
numerically and determine the tunneling probability for the birth of a
asymptotically DeSitter, inflationary universe, initially, as a function of the
mean energy of the initial wave-function. Then, we verify that the tunneling
probability increases with the cosmological constant, for a fixed value of the
mean energy of the initial wave-function. Our treatment of the problem is more
general than previous ones, based on the WKB approximation. That is the case
because we take into account the fact that the scale factor ($a$) cannot be
smaller than zero. It means that, one has to introduce an infinity potential
wall at $a = 0$, which forces any wave-packet to be zero there. That condition
introduces new results, in comparison with previous works.
