equations and coefficients for mode choice:

Car Mode: Ucar$=$Ucar$={}_{\text{c}\text{a}\text{r}\text{,}0}+{}_{\text{c}\text{a}\text{r}\text{,}1}$ Travel Time $+{}_{\text{c}\text{a}\text{r}\text{,}2},x$ Cost

Bus Mode: $U_{\text{b}\text{u}\text{s}}={}_{\text{b}\text{u}\text{s},0}+{}_{\text{b}\text{u}\text{s},1}$ Travel Time $+{}_{\text{b}\text{u}\text{s},2}$ Cost

Train Mode: $U_{\text{t}\text{r}\text{a}\text{i}\text{n}}={}_{\text{t}\text{r}\text{a}\text{i}\text{n},0}+{}_{\text{t}\text{r}\text{a}\text{i}\text{n},1}$ Travel Time $+{}_{\text{t}\text{r}\text{a}\text{i}\text{n},2}$ Cost

Where:

$U_{\text{c}\text{a}\text{r}},U_{\text{b}\text{u}\text{s}},U_{\text{t}\text{r}\text{a}\text{i}\text{n}}=$ Utilities for car, bus, and train modes, respectively

Travel Time $=$ Travel time for the respective mode

Cost $=$ Cost associated with the respective mode

The coefficients are given as follows:

Car Mode: ${}_{\text{c}\text{a}\text{r}\text{,}0}=2\mathrm{.}5,{}_{\text{c}\text{a}\text{r}\text{,}1}=-0\mathrm{.}1,{}_{\text{c}\text{a}\text{r}\text{,}2}=-0\mathrm{.}05$

Bus Mode: $$ bus $,0=1\mathrm{.}8,$ bus, $1=-0\mathrm{.}08,$ bus, $2=-0\mathrm{.}03$

Train Mode: ${}_{\text{t}\text{r}\text{a}\text{i}\text{n},0}=2\mathrm{.}2,{}_{\text{t}\text{r}\text{a}\text{i}\text{n}\text{,},1}=-0\mathrm{.}09,$ train, $2=-0\mathrm{.}04$

Given a specific scenario with the following travel times and costs:

Car Mode: Travel Time $=30$ minutes, Cost $=$$$8$

Bus Mode: Travel Time $=45$ minutes, Cost $=$$$2$

Train Mode: Travel Time $=35$ minutes, Cost $=$$$10$

Calculate:

A$.$ the probabilities of choosing each mode $($round your answers to two decimal places$)$

B$.$ how many car trips could be reduced if the bus mode cost is reduced by $50\%$