A driver encounters two traffic lights on the way to work eachmorning. Each ligh

Question

A driver encounters two traffic lights on the way to work eachmorning. Each light is either red, yellow, or green. The probabilities of the various combinations is given in thefollowing table

                   Second Light

First Light

R

Y

G

R

0.30

0.04

0.16

Y

0.05

0.01

0.04

G

0.15

0.05

0.20

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 that the first light is red, find the probability that thesecond light is green

Given that the second light is yellow, find the probability thatthe first light is red.

                   Second Light

First Light

R

Y

G

R

0.30

0.04

0.16

Y

0.05

0.01

0.04

G

0.15

0.05

0.20

Explanation / Answer

1)For the probability the first light is red add up thepossibilities when it is red=RR+RY+RG=.3+.04+.16=.5 2)Add up the column for the second light beinggreen:RG,YG,GG=.16+.04+.2=.4 3)For this one:RR+YY+GG=.3+.01+,2=.51 4)For this one RG/(RR+RY+RG)=.16/(.3+.04+.16)=.32 5)For this one RY/(RY+YY+GY)=.04/(.04+.01+.05)=.4

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