6. A driver encounters two traffic lights on the way to work each morning. Each

Question

6. A driver encounters two traffic lights on the way to work each morning. Each light is either red, green or yellow. The probability of the various combination ofcolors is given the following table Second Light First Light R Y G 0.30 0.04 0.16 0.05 0.01 0.04 0.15 0.05 0.20 a. b. c. d. What is the probability that the first light is red? What is the probability that the second light is green? Find the probability that both lights are the same color. Given the first light is rd, find the probability that the second light is green. e. Given the second light is yellow, find the probability that the first one is red

Explanation / Answer

from given distribution:

a) probability =P(R1) =0.3+0.04+0.16 =0.5

b)P(G2) =0.4

c) P(R1R2)+P(Y1Y2)+P(G1G2) =0.3+0.01+0.2=0.51

d) P(G2|R1) =P(R1 n G2)/P(R1)=0.16/0.5 =0.32

e) P(R1|Y2) =0.04/0.1 =0.40

second R Y G total first R 0.3 0.04 0.16 0.5 Y 0.05 0.01 0.04 0.1 G 0.15 0.05 0.2 0.4 total 0.5 0.1 0.4 1

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