A particularly 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