Exercise 3.8. (TRAFIC LIGHTS) A driver encounters two traffic lights on the way

Question

Exercise 3.8. (TRAFIC LIGHTS) A driver encounters two traffic lights on the way to work 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 foll FirstLight Second Light DGC+4000 0.04 0.16 DGC DGC+5000 0.05 0.04 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. Instructor : Sarjinder Singh

Explanation / Answer

from above information below is probability distribution:

a) probability that first light is red =0.3019

b) probability that second light is green =0.5248

c) probability that both light of same color =P(RR)+P(YY)+P(GG) =0.1019+0.0832+0.3248 =0.5100

d) probability of second light green given first light is red =0.16/0.3019 =0.5299

second light first light R Y G total R 0.1019 0.0400 0.1600 0.3019 Y 0.0500 0.0832 0.0400 0.1732 G 0.1500 0.0500 0.3248 0.5248 total 0.3019 0.1732 0.5248 1.0000

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