A cell phone battery can be produced by machine A, machine B, or machine C. Twenty percent of the time the battery will be produced by machine A, 45% by machine B, and 35% by machine C. A quality control analyst inspects the batteries after production and finds that machine A makes defective batteries 10% of the time, where machines B and C each makes defective batteries 8% of the time.
One cell phone battery is randomly selected from the production line, what is the probability the battery is defective and produced by machine C? Round your answer to three decimal places.