Question $1($Please show all the steps and final answer$)$

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 mode

b$)$ The zone's expected auto modal share using naive aggregation.

$V_a=0\mathrm{.}25-0\mathrm{.}1IVT{T}_a-0\mathrm{.}20OVT{T}_a-0\mathrm{.}0007(\frac{OPT{C}_a}{\text{I}\text{N}\text{C}})+0\mathrm{.}25AO$

$V_t=-0\mathrm{.}11IVT{T}_t-0\mathrm{.}2OVT{T}_t-0\mathrm{.}0007(\frac{OPT{C}_a}{\text{I}\text{N}\text{C}})$

Eq$.1$

Eq$.2$

where:

IVTT $=$ in$-$vehicle travel time

INC$=$ household income

OVTT $=$ out$-$of$-$vehicle travel time

$AO=$ household auto$-$ownership

OPTC $=$ out$-$of$-$pocket travel cost

Table $1$: Individual Observations

$\backslash$table$[[$Obs$.$ #$,$IVTT ${?}_a,IVT{T}_t,$OVTT ${?}_a,$OVTT ${?}_t,$OPTC ${?}_a,$OPTC ${?}_t,IN{C}^N,AO$