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: .