So there are two cases 1.you pike first and 2.your friend pick first

case 1: you pike first

     p(car)=1/3 


case 2: your friend pike first

     in order for you to get a car, your friend have to either pike goat#1 or goat#2.
     your friend pike goat#1 and you pike a car
     p(car case 1)=1/3*1/2
     your friend pike goat#2 and you pike a car
     P(car case 2)=1/3*1/2
     
     in order to get the total possibility, you add the p(car case 1) and p(car case 2)together
     we get P(car)=1/6+1/6=1/3

so i conclude the possibility is the same

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Ruth Enoch, PhD Mathematics