Recall that Batman failed his superhero test, despite having a good feeling abou
ID: 3225979 • Letter: R
Question
Recall that Batman failed his superhero test, despite having a good feeling about it. the Joker decided to reprogram all of the traffic lights in Gotham. They now randomly go from one color to the next after a fixed time of 30 seconds. He programmed them to change independently according to the following transition matrix [.1 0 .9 .2 .3 .5 0 .4 .6] where the colors are ordered Green, Yellow. Red (i.e p_2.3 = .5 represents the probability the light changes from yellow to red) (a) If the light is yellow now, what is the probability that it will be green next? (b) If the light is yellow now, what is the probability that it will be red 2 after 2 changes? (i.e. find p^(2) and then p_3^(2))Explanation / Answer
a) If the light is yellow now, probability that it will be green next would be:
p2,1 = this would be the the first element of the second row of the transition matrix. Therefore we get:
p2,1 = 0.2
0.2 is the required probability here.
b) If the light is yellow now, it will be red after 2 changes in the following ways:
Therefore the total probability required here is 0.18 + 0.15 + 0.30 = 0.63
0.63 is the required probability here.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.