Assuming the conventional 1.5 - 4.5 K IPCC uncertainty range (and its translation by Wigley & Raper, 2001, into
a lognormal pdf assuming the range to be a 90 % confidence interval), this risk of overshooting 2 °C is about 75 % (13 %) in equilibrium for 550ppm (400ppm) CO2 equivalence stabilization.
I'll have to spend some time on a few parts, but it is certainly a good reminder that Gaussians are not guaranteed, and in fact, I was interested to see
PDFs (as on p. 7) that seem to look more like
lognormals, at least by eyeball, and if so, then the question arises of doing the log - scale transform to see if the results indeed do OK on normality tests, and hence retrieve the good properties we all love.