1Probability that A wins all the games = (2/3)4
Prob. that A loses the fifth game = (1/3)(2/3)3
Prob. that A loses the second game = (1/3)2(2/3)2
Prob. that A loses the Third game = (1/3)2(2/3)2
Prob. that A loses the fourth game = (1/3)2(2/3)2
Total Probability of the given event = 36/81
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