Question
Asked Sep 18, 2019
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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?

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Expert Answer

Step 1

Let xi denotes the probability of hitting red light in ith intersections
G...

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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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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