Asteroids with a diameter of ~50m are estimated to collide with Earth every ~750 years. Such an event is expected to generate an airburst (atmospheric explosion) with an energy equal to 5.2 Megatons of TNT (or roughly 3250x the energy of the nuclear bomb dropped on Hiroshima in World War II).

a) Without any information about past events, what is the probability that such an event will happen in your lifetime? (Assume that the future average longevity of Americans is 80 yrs.)

b) The last time an asteroid of this size hit Earth was fairly recently, in 1908 over Tunguska, Siberia. This event is estimated to have knocked over ~80 million trees and is the largest impact event in recorded history, easily capable of obliterating a large city. Given that this event occurred, what is the probability of a second impact of this magnitude during your lifetime?

c) Cities cover approximately 0.5% of the Earth's land area, which itself constitutes 29% of the total surface of the planet. What is the probability that the second explosion in part (b) occurs over a city? Assume an equally likely probability of impact over the entire surface.