Consider the mode split model for work trips in a region as follows: Va = a1 + aIVTTa + 04OVTTa + 05(OPTC/INC) + 6 AO Vb = VTTb + 4OVTTb + 5(OPTC/INC) where coefficients are as follows: Auto constant IVTT (min) OVTT (min) OPTC/INC AO Auto coefficient 0.25 -0.10 -0.20 -0.0007 0.25 Bus coefficient 0.0 -0.11 -0.20 -0.0007 0.25 Mode choice demand analysis is to be performed for a suburban where the population of 1000 workers classified into 4 groups; two income levels (expressed as level 1 and 2) and two auto ownership is either 1. Studies show the following distribution of the workers groups: O Auto 1 Auto Variable Income level 1 IVTT (min) OVTT (min) OPTC (S) (Group 1) 40% (Group 3) 20% The characteristics of both the auto and bus modes are as follows: Auto 16 2 Income level 2 (Group 2) 30% (Group 4) 10% 2.00 Bus 26 2 0.50 a) Find the probability of an individual in each of the four groups of choosing transit. b) What is the estimated total number of trips using transit? You may use naive aggregation method.