A $1.5\times {10}^9$ years old rock contains ${}^{238}\mathrm{U}$ which disintegrates to form ${}^{206}\mathrm{Pb}$. Assume that there was no lead in the rock initially and it is the only stable product formed by the decay. Calculate the ratio of the number of nuclei of lead to that of uranium. [Given, half-life of ${}_{}{}^{238}\mathrm{U}$ =  $4.5\times {10}^9$ years, $2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\approx 1.26$]