A driver encounters two traffic lights
A driver encounters two traffic lights on the way to work each morning. Each light is either red, yellow, or green. The probabilities of the various combinationsof colors is given in the following
table:
Second light
First LightRYG
R0.300.040.16
Y0.050.010.04
G0.150.050.20
a. What is the probability 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.
e. Given that the second light is yellow, find the probability that the first light was red.
Homework Answers
Probability that the 2nd light is green is:0.16+0.04+0.20=0.4
Probability that both lights are same colour: 0.30+0.01+0.20=0.51
Probability that 2nd light is green if 1st is red is:0.16/(0.16+0.04+0.30)=0.32
The probability that 1st light is red given 2nd is yellow is:0.04/(0.04+0.01+0.05)=0.4
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