The power generation plant of a ship is outfitted with two identical diesel-generator sets. One single set running stand-alone can meet the full power requirement of the vessel. The engine of each set has a malfunction probability of 25% and the generator of 10%. In case one set breaks down there is a 50% probability of it being repaired but it will run again only if repaired and its subsystems do not further malfunction upon startup. Calculate the probability of an electric power outage shipboard.

probability of an electric power outage shipboard is 0.075 or 7.5 %

Step-by-step explanation:

Given the data in the question;

Probability of engine malfunction = 25% = 0.25

Probability of generator malfunction = 10% = 0.1  

Probability of generator being repaired = 50% = 0.5

probability of an electric power outage shipboard = ?

To get the probability of an electric power outage shipboard, we use the expression;

probability of an electric power outage = 2 × p( Probability of generator malfunction ) × p( Probability of generator being repaired ) × ( 1 - p( Probability of engine malfunction ) )

so we substitute in our given values;

probability of an electric power outage = 2 × 0.1 × 0.5 × ( 1 - 0.25 )

probability of an electric power outage = 2 × 0.1 × 0.5 × 0.75

probability of an electric power outage = 0.075 or 7.5 %