Hello, dear members!
Q: Single bus runs between points 0 and 1 with constant speed. Passenger comes at random time to random point '0<x1<1' and wants to go to random point '0<x2<1' (points x1 and x2 are equally distributed along [0,1]). Is it right that when bus reached point 'x1' at first time it will go into the opposite direction (than x1->x2) with higher probability?
A: It is obvious that probability of passenger's bad luck is 1-integ_{0}^{1}(2*(x1*(1-x1)))dx1=1-1/3=2/3
But does more intuitive solution exist to explain this paradox to a child?
Q: Single bus runs between points 0 and 1 with constant speed. Passenger comes at random time to random point '0<x1<1' and wants to go to random point '0<x2<1' (points x1 and x2 are equally distributed along [0,1]). Is it right that when bus reached point 'x1' at first time it will go into the opposite direction (than x1->x2) with higher probability?
A: It is obvious that probability of passenger's bad luck is 1-integ_{0}^{1}(2*(x1*(1-x1)))dx1=1-1/3=2/3
But does more intuitive solution exist to explain this paradox to a child?