Teenager Mike wants to borrow the car. He can ask either parentfor permission to take the car. If he asks his mom, there is a 20%chance she will say â€yes,†a 30% chance she will say â€no,†and a50% chance she will say, â€ask your father.†Similarly, that chancesof hearing â€yesâ€/â€noâ€/â€ask your mother†from his dad are 0.1, 0.2,and 0.7 respectively. Imagine Mike’s efforts can be modeled as aMarkov chain with state (1) talk to Mom, (2) talk to Dad, (3) getthe car (â€yesâ€), (4) strike out (â€noâ€). Assume that once eitherparent has said â€yes†or â€no,†Mike’s begging is done.
1. Construct the one-step transition matrix for this Markovchain.
2. Identify the absorbing state(s) of the chain.
3. Determine the mean times to absorption.
4. Determine the probability that Mike will eventually get thecar if (1) he asks Mom fist and (2) he asks Dad first. Whom shouldhe ask first?
