An investor has two investments A and B. The investor believes that investment A is equally likely to increase by $1,000 or to decrease by $1,000 by the end of the year. The investor also believes that investment B is equally likely to increase by $2,000 or decrease by $2,000 by the end of the year. Let X represent the total amount of change in investments A and B. Assume that these investments perform independent of each other. Find the probability of X.