Given the following vector of state probabilities and the accompanying matrix of transition probabilities,find the next period vector of state probabilities.
(0.4 0.4 0.2) 
Definitions:
Urinary Tract Infection
An infection in any part of the urinary system, including kidneys, ureters, bladder, or urethra, most commonly caused by bacteria.
Drainage Bag
A medical device used to collect fluid that has been drained from the body, typically used in surgeries or with catheters.
Catheter Tubing
Flexible tubes used in medical settings to administer fluids, medications, or gases to patients, or to drain bodily fluids.
Urinary Diversion
A surgical procedure that redirects urine flow from its normal pathway due to medical conditions affecting the bladder.
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