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Social ScienceA Driver keeps goes through 3 intersections. The probabibilty of hitting a red light at each are 0.2, 0.4, and 0.4 respectively. What is the probabibility of hitting at least two red lights?
A Driver keeps goes through 3 intersections. The probabibilty of hitting a red light at each are 0.2, 0.4, and 0.4 respectively. What is the probabibility of hitting at least two red lights?
Expert Answer
Let xi denotes the probability of hitting red light in ith intersections
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Cases for hitting at least 2 red lights are hitting 2 red lights hitting 3 red lights Cases of hitting 2 red lights Р(X) x Р(Х2) х Р(Х3) + P(X,) x Р(X) x Р(Х3) + P(X,) Х Р(X2) х Р(Х3) = 0.2 x 0.4 x 0.6 + 0.2 x 0.6 x 0.4 + 0.8 x 0.4 x 0.4 = 0.224 of hitting 3 red lights = cases — Р(X) х Р(Х2) Х P(X3) = 0.2 x 0.4 x 0.4 = 0.032 Probability of hitting at least 2 red lights are = 0.224 0.032 =0.256
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