HW 210 A particularly long traffic light on your morning com

HW 2.10. 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? (b) What is the probability that the light is nut green for 30 consecutive mornings? (c) What Is the probability that tar more than two green lights will be observed among the first 3 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]