A bomb lying in a storehouse explodes at the beginning of each minute with probability 1 3 , independently of the history.

1. Devise a Markov chain describing the evolution of the bomb. Write down the transition probabilities and the initial distribution.

2. What is the distribution of the time (in minutes) from the moment the bomb is placed in the storehouse until the explosion?

Draw the transition graph for the Markov chain , and write down the transition matrix.