During a major storm seawater has entered the cable conduit for a tidal power station. The seawater may have damaged the insulation greatly increasing the likelihood of a short circuit. The power company needs to decide whether or not to replace the cables in the conduit. If there is a short circuit then the whole conduit will be seriously damaged and need to be reconstructed. The cost of replacing the cables is $30 000. The cost of replacing the complete conduit is $500 000. If the cable is not replaced the probability of a short circuit occurring is estimated to be 0.1. If it is replaced this drop to 0.000 01. It is possible to send a remote camera through the conduit to inspect the cable at a cost of $5 000. This inspection is not 100% accurate in detecting damage and so

P(The inspection detects damage | A short circuit will occur) = 0.9

P(The inspection detects damage | A short circuit will not occur) = 0.05

A) Draw the decision tree for this situation.

B) Determine the remaining required probabilities and mark clearly on your tree.

C) Determine the best course of action to follow.