Mathematics, 20.10.2020 20:01 finlchey3860
Suppose each day that you drive to work a traffic light that you encounter is either green with probability 3/8, red with probability 1/2, or yellow with probability 1/8, independent of the status of the light on any other day. If over the course of five days, G, Y, and R denote the number of times the light is found to be green, yellow, or red, respectively, what is the probability that P[G=2, Y=1, R=2] ? Also, what is the probability P[G=R]? [15%]. Hint: consider sequences possible in a five-day observations
Answers: 3
![P(G = 2 , Y= 1 , R = 2) = \frac{5!}{ 2! * 1! * 2!} * [\frac{3}{8} ]^2 * [\frac{1}{8} ]^1 * [\frac{1}{2} ] ^2](/tpl/images/0824/9269/892b3.png)
![P( G = 0 , Y = 5 , R = 0) = \frac{5!}{ 0! * 5! * 0!} * [\frac{3}{8} ]^0 * [\frac{1}{8} ]^5 * [\frac{1}{2} ] ^0](/tpl/images/0824/9269/6a5f2.png)
![P( G = 1 , Y = 3 , R = 1)= \frac{5!}{ 1! * 3! * 1!} * [\frac{3}{8} ]^1 * [\frac{1}{8} ]^3 * [\frac{1}{2} ] ^1](/tpl/images/0824/9269/e4c75.png)
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