Question

A student takes the same street from his home to the university every day. There are 3 streetlights along the way, and he has noticed the following Markov dependence. If he sees a green light at an intersection, then 77% of time the next light is also green. However, if he sees a red light, then 77% of time the next light is also red. (Assume the chance of him seeing a yellow light is zero.) If the first light is green, what is the probability that the third light is red

Answer 1

0.3542 = 35.42% probability that the third light is red

Explanation:

For each light:

If it is green, 77% probability that the next is green.

If it is red, 77% probability that the next is red.

If the first light is green, what is the probability that the third light is red?

These following outcomes are desired, for the second and third lights:

G - R(0.77, then 1 - 0.77 = 0.23 probability)

R - R(0.23, then 0.77 probability).

So the desired probability is:

`p = 0.77*0.23 + 0.23*0.77 = 0.3542`

0.3542 = 35.42% probability that the third light is red