Two armies A and B are at war. Army A has 2 identical tanks and Army B has 2 identical tanks (but different than those of Army A). Army A's tanks have a probability of 1/2 of destroying the tank at which they fire. Army B's tanks have a probability of 1/3 of destroying the tank at which they fire. At each round all the available tanks fire once. Those tanks that are not hit continue to the next round. If both armies have 2 tanks each, then each tank fires at a different opposing tank. If one army has one tank and the other army has 2 tanks, then the first tank fires at one of the other tanks at random. If one rmy as 2 tanks and the other army has only one tank, then both tanks fire at the single enemy tank. anks fire at each other simultaneously. Form a Markov chain by taking as states the number of tanks of ch type that are still available. Don't solve the game.

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Two armies A and B are at war. Army A has 2 identical tanks and Army B has 2 identical tanks (but
different than those of Army A). Army A's tanks have a probability of 1/2 of destroying the tank at
which they fire. Army B's tanks have a probability of 1/3 of destroying the tank at which they fire. At
each round all the available tanks fire once. Those tanks that are not hit continue to the next round. If
both armies have 2 tanks each, then each tank fires at a different opposing tank. If one army has one
tank and the other army has 2 tanks, then the first tank fires at one of the other tanks at random. If one
army as 2 tanks and the other army has only one tank, then both tanks fire at the single enemy tank.
Tanks fire at each other simultaneously. Form a Markov chain by taking as states the number of tanks of
each type that are still available. Don't solve the game.
Transcribed Image Text:Two armies A and B are at war. Army A has 2 identical tanks and Army B has 2 identical tanks (but different than those of Army A). Army A's tanks have a probability of 1/2 of destroying the tank at which they fire. Army B's tanks have a probability of 1/3 of destroying the tank at which they fire. At each round all the available tanks fire once. Those tanks that are not hit continue to the next round. If both armies have 2 tanks each, then each tank fires at a different opposing tank. If one army has one tank and the other army has 2 tanks, then the first tank fires at one of the other tanks at random. If one army as 2 tanks and the other army has only one tank, then both tanks fire at the single enemy tank. Tanks fire at each other simultaneously. Form a Markov chain by taking as states the number of tanks of each type that are still available. Don't solve the game.
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