A certain utility firm has noticed that a residential customer's bill for one month is dependent on the previous month's bill.The observations are summarized in the following transition matrix. 
The utility company would like to know the long-run probability that a customer's bill will increase,the probability the bill will stay the same,and the probability the bill will decrease.
Definitions:
Family Planning
The practice of controlling the number and spacing of offspring through the use of contraception or fertility control.
Vas Deferens
The duct through which sperm travels from the testicle to the urethra, essential for the delivery of male gametes to the female reproductive tract.
Male Sterilization
A form of contraception involving a surgical procedure (vasectomy) that makes a man permanently unable to father children.
Laparoscopy
A form of tubal ligation using a viewing lens (the laparoscope) to locate the fallopian tubes and another instrument to cut or block and close them.
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