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A local traffic light is set so that it cycles between 30 seconds of red and 30 seconds of green. What is the probability of randomly hitting a red light more than 25 times in n = 40 trips through the intersection?

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Answer: 0.04

Step-by-step explanation:

Number of trips (n) = 40

Red = 30 seconds, Green = 30 seconds

P(red) = p(green) = 30/ (30+30) = 0.5

P(not red) = p(not green) = 1 - 0.5 = 0.5

P(x) = nCx * p^x * (1-p)^(n-x)

n = number of trials

x = number of outcome desired

P = probability of success of desired outcome

P(X > 25) = P(26) + p(27) + p(28) +.... + p(40)

Hence, to save computation time, we use the binomial distribution probability calculator :

P(X > 25) = 0.04