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At a certain intersection, the traffic light is red for 15 seconds, yellow for 5 seconds and green for 30 seconds. Find the probability that, of the next eight cars that arrive randomly at the light, exactly three will be stopped by a red light.

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Answer: 0.254

Step-by-step explanation:

Given that:

Number of cars = number of trials (n) = 8

Number that will be stopped by a red light = Numbe rof successes (r) = 3

Probability of success :

Red light = 15 seconds ; yellow = 5 seconds ; green = 30 seconds

P(red) = p(success) = p = 15 / (15 + 5 + 30) = 15/50 = 3 /10 = 0.3

1 - p = 1 - 3/10 = 7/10 = 0.7

Using the binomial probability relation:

p(exactly 3):

P(8, 3) = 8C3 * p^3 * (1-p)^(8-3)

P(8, 3) = 8C3 * p^3 * (1-p)^5

P(8, 3) = 56 * 0.3^3 * 0.7^5

= 0.25412

= 0.254

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