Question $1$:Equations $1$ & $2$ present the utility functions for auto and transit modes, respectively. Given Table $1,$ which shows utility function variables for individual observations in a zone, calculate the following:a$)$The probability of each observation using the auto modeb$)$The zones expected auto modal share using naive aggregation.$=0\mathrm{.}250\mathrm{.}1\backslash$times $0\mathrm{.}20\backslash$times $0\mathrm{.}0007\backslash$times $()+0\mathrm{.}25\backslash$times Eq$.1=0\mathrm{.}11\backslash$times $0\mathrm{.}2\backslash$times $0\mathrm{.}0007()$ Eq$.2$where:IVTT $=$ in$-$vehicle travel timeINC $=$ household incomeOVTT $=$ out$-$of$-$vehicle travel timeAO $=$ household auto$-$ownershipOPTC $=$ out$-$of$-$pocket travel cost