Hello, jojo_jojo!

Suppose that each day the price of a stock moves up $1 with probability 1/3

and moves down $1 with probability 2/3.

If the price fluctuations from one day to another are independent,

what is the probability that after six days the stock has its original price?

We are given: .

If the stock is back to original price,

. . there were three Ups and three Downs, in some order.

There are: . possible orders.

The probability of 3 Ups and 3 Downs is: .

Therefore: .