Motivated by the recent determinations of the Hubble constant (H_0) from observations of Cepheid variables in NGC4571 and M100, we plot the Tinsley diagram with level curves of the cosmological constant (Λ). Based on current estimates of the absolute ages of globular clusters we conclude that Λ > 0 and, irrespective of the background spatial curvature, the universe will not recollapse. These conclusions hold for both relativistic and Newtonian models and are independent of the density parameter.