Suppose on a road trip to Texas you observe that three out of every four trucks on the road are followed by a car, while only one out of every five cars is followed by a truck. What fraction of vehicles on the road are trucks
Suppose on a road trip to Texas you observe that three out of every four trucks on the road are followed by a car, while only one out of every five cars is followed by a truck. What fraction of vehicles on the road are trucks?
There are several methods to solve the problem. I am using Markov chain method here. Hope you are already familiar with it.
The probability is 3/4 if a truck goes by the next vehicle will be a car and and the probability will be 1/4 if it is a truck.If a car goes by the next vehicle will be a car with probability 4/5 and will be a truck with probability 1/5. We may set this up as a Markov chain with two states Truck and car. Transition probability matrix can be written as:
Truck Car
Truck 1/4 3/4
Car 1/5 4/5
Assume that Markov chain has two states truck = 0 and car =1, and transition probability matrix can be rewritten as:
0 1
0 1/4 3/4
1 1/5 4/5
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