Question

In: Statistics and Probability

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

5. 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 combinations of colors is given in the following table:

		Second Light
First Light	R	Y	G
R	0.31	0.02	0.18
Y	0.02	0.03	0.03
G	0.14	0.04	0.23

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 of the same color.

d) Given that the first light is red, find the probability that the second light is green.

Expert Solution

a) What is the probability that the first light is red?

The probability that the first light is red = P( first light is Red ) = 0.31 + 0.02 + 0.18 = 0.51

b) What is the probability that the second light is green?

The probability that the second light is green = P ( second light is Green ) = 0.18 + 0.03 + 0.23 = 0.44

c) Find the probability that both lights are of the same color.

= P(R,R) + P(Y, Y) + P(G, G) = 0.31 + 0.03 + 0.23 = 0.57

d) Given that the first light is red, find the probability that the second light is green.

P( second light is green | first light is red ) = P( second light is green and first light is red ) / P( first light is red )

Let P( second light is green and first light is red ) = 0.18

P( first light is red ) = 0.51

Therefore, P( second light is green | first light is red ) = 0.18/0.51 = 18/51 = 6/17 = 0.352941

orchestra answered 10 months ago

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

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