A critical piece of equipment operating at an arctic base has an engine, transmission and power-take off (PTO) units. For it's mission, all three units must be functional, otherwise the equipment is unusable. Under typical temperatures, the probabilities failure in 5 years are 0.07, 0.03 and 0.02. Under extreme cold, the probabilities increase to 0.10, 0.05 and 0.03 respectively. The equipment is expected to be operated in extreme cold 20% of the time and normal temperatures the remainder of the time. If the transmission fails, the probability that the PTO unit fails is doubled.

If the equipment fails in 5 years, what is the probability that the PTO unit has failed?