In this question , the probability of x moving to the right is more than what y moves to the right....so the deciding factor for the possibility of y being on the right of x is the no. of times x moves to the left

Let Lx and Ly be the probability of x and y to move to the left

Probability that x moves more towards left than y is given by binomial expansion

Prob. =⁵C₀Lx⁵+⁵C₁Lx⁴Ly + ⁵C₂Lx³Ly²

Therefore by putting Lx=1/3 and Ly=1/2

We get prob. = 31/243

 

If u have any doubt or any other answer....plz reply