5. A commuter passes through three traffic lights on the way to work. Each light

Question

5. A commuter passes through three traffic lights on the way to work. Each light is either red, yellow, or green. An experiment consists of observing the colors of the three lights. List the 27 outcomes in the sample space. (27 points) Let A be the event that all the colors are the same. List the outcomes in A. (4 a. b. c. Let B be the event that all the colors are different. List the outcomes in B. (4 d. points) Let C be the event that at least two lights are green. List the outcomes in C. (4 points)

Explanation / Answer

a) sample space

S={(red,red,red),(red,red,green),(red,red,yellow),(red,green,red),(red,yellow,red),(red,green,green),

(red,yellow,yellow),(red,yellow,green),(red,green,yellow),(green,red,red),(green,red,green),(green,red,yellow),(green,green,red),(green,yellow,red),(green,green,green),(green,yellow ,yellow),(green,yellow,green),(green,green,yellow),(yellow,red,red),(yellow,red,green),(yellow,red,yellow),(yellow,green,red),(yellow,yellow,red),(yellow,green,green),(yellow ,yellow ,yellow),(yellow,yellow,green),(yellow,green,yellow)}

b)

A={(red,red,red),(green,green ,green ),(yellow,yellow ,yellow )}

c)

B={(red,yellow,green),(red,green,yellow),(green,red,yellow),(green,yellow,red),(yellow,red,green),(yellow,green,red)}

d)

C={(red,green,green),(green,red,green),(green,green,red),(green,green,green),(green,yellow,green),(green,green,yellow),(yellow,green,green)}

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