When a very large star reaches the end of its life it explodes, causing a supernova, a very intense burst of radiation that is sufficient to destroy almost all life on planets of nearby stars. Some simple organisms may remain, but all animals and plants are destroyed and evolution has to start again from the simple organisms. On Earth it took 100 million years to get from such a simple organism to humans.

a) In our part of the galaxy (toward the edge), supernovas sufficiently powerful to have such an impact on life on Earth occur at random on average every 500 million years. Suppose such a supernova occurred tomorrow. What is the probability of another one occurring in the next 100 million years and thus delaying the evolution of human-like life? 

b) At the centre of our galaxy, stars are closer together. There, supernovas of this destructive power occur on average once every 50 million years. Suppose such a supernova occurred tomorrow, wiping out all but simple organisms on a planet. What is the probability of no supernova occurring in the next 100 million years and thus allowing human-like life to evolve?