DGC = 415 Exercise 3.8. (TRAFIC LIGHTS) A driver encounters two traffic lights o

Question

DGC = 415
Exercise 3.8. (TRAFIC LIGHTS) A driver encounters two traffic lights on the way to each morning. Each light is either a red, yellow, or green. Fig. 3.8. Motor Cyclist First Light Second Light The probabilities of the various combinations of colors are given in the following table: First Light Second Light DGC IDGC+4000 =| 0.04 0.16 DGC DGC+5000 0.04 0.05 0.15 0.05 (a) What is the probability that the first light is red? (b) What is the probability that the second light is green? (c) Find the probability that both lights are the same color. (d) Given that the first light is red, find the probability that the second light is green.

Explanation / Answer

from above:

a) probability that first light is red =0.2940

b) probability that second light is green =0.5394

c) probability that both light are same color =P(RR)+P(YY)+P(GG) =0.0940+0.0766+0.3394 =0.5100

d) probability that second light green ; given first light is red =0.1600/0.2940 =0.5442

second light first light R Y G total R 0.0940 0.0400 0.1600 0.2940 Y 0.0500 0.0766 0.0400 0.1666 G 0.1500 0.0500 0.3394 0.5394 total 0.2940 0.1666 0.5394 1.0000

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