Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 05 (b)
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Question B 05 (b) 

Suppose four towns are connected by roads in the configuration shown below. A random driver wakes up every morning and flips a coin. If the coin is heads, she stays where she is for the day. If the coin is tails, she drives to the next town, choosing one of the roads with no preference. (For example, if she leaves Town A, she is equally likely to go to Town B or Town C, but she will not go to Town D that day.) (b) If the driver starts in Town A, what is the probability she will be in Town A two days later? 
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If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Consider all the possibilities after one day, then for each one find the possibility that goes to A at the second day. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. At the first day, from matrix , driver can end up with A, with chance A to A is (p=1/2). At the second day, A move back to A is also 1/2. This routine (AAA)has chance of . 1st day, driver can also end up with B, A to B is (p=1/4), under this case, if driver wanna go back to A at second day, the chance from B to A is (p=1/6). This routine (ABA)has chance of . Same, the routine (ACA)has chance of . The routine (ADA)has chance of . answer: 
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