Aparticularly long traffic light on your morning commute is green on 20% of the mornings. assume that each morning represents an independent trial. (a) what is the probability that the first morning that the light is green is the fourth morning?

Given:
p=0.2
independent Bernoulli trials (green=success)

Need to find: probability that first three trials are failures, and the fourth one is a success.

Method: The conditions given fit the requirements of the geometric distribution, where for k failures before the first sucess
P(k)=(1-p)^k*p
=(1-0.2)^3*0.2
=0.8^3*0.2
=0.1024