A particularly long traffic light on your morning commute is

A particularly long traffic light on your morning commute is green on 40% of the mornings. Assume that each morning represents an independent trial. What is the probability that the first morning that the light is green is the third morning? What is the probability that the light is not green for 5 consecutive mornings? What is the probability that no more than two green lights will be observed among the first 5 mornings?

Solution

Let G = the light is green

a)

P(G\', G\', G) = (1-0.4)(1-0.4)(0.4) = 0.144 [answer]

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b)

P(5 consecutive not green) = (1-0.4)^5 = 0.07776 [answer]

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c)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    5      
p = the probability of a success =    0.4      
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.68256 [answer]