A Toyota dealer consumes four kinds of engine oil A, B, C and D. This dealer...

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A Toyota dealer consumes four kinds of engine oil A, B, C andD. This dealer buys its consumption each week. The dealer neverbuys the same brand in successive weeks, except brand D. If thedealer buys engine oil D then with same probability it can buy allkinds of engine oils next week. If the dealer perches brand C thennext week it will buy D. However, if the dealer buys engine oil Bthen the next week it is four times as likely to perches A as theother brands and finally if the dealer buy engine oil A it will buyD or C with same probabilities. What is the probability thatmentioned dealer buys oil C when we know that oil B was purchasedthree weeks ago?

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We can model the problem as Mrakov chain with states A B C andDThe tratnsition probability from state A to state C or D is12The tratnsition probability from state A to state Aor B See Answer

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