It can be presumed that the life span in years of a certain brand of lightbulbs follows the Poisson process assumptions. Suppose that the mean life span till failure is known to be 0.7 years. A tester makes random observations of the life times of this particular brand of lightbulbs and records them one by one as either a success if the life time exceeds 1 year, or as a failure otherwise.

Determine the probability that a randomly tested bulb lasts more than 1 year:

Determine probability that the first success occurs in the fifth observation:

Determine the probability that the second success occurs in the 8th observation given that the first success occurred in the 3rd observation:

Determine the probability that the first success occurs in an odd-numbered observation: