Strong earthquakes occur according to a Poisson process in a metropolitan area with a mean rate of once in 50 year. There are three bridges in the metropolitan area. When a strong earthquake occurs, there is a probability of 0.3 that a given bridge will collapse. Assume the events of collapse between bridges during a strong earthquake are statistically independent; also, the events of bridge collapse between earthquakes are also statistically independent.
What is the probability of "no bridge collapse from strong earthquakes" during the next 20 year?