Answer: 0.254
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