A team has probability 2/3 of winning a game whenever it plays. If the team plays 4 games then the probability that it wins more than half of the games is

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Let p be the probability that the team wins a game. Let $q = 1 - p$ . Then the random variable "number of wins" follows the binomial distribution $P (X = K) =^{4} C_{k} q^{4 - k} p^{k}, k = 0, 1, 2, 3, 4$ .

Required probability $=^{4} C_{3} (\frac{1}{3}) (\frac{2}{3})^{3} +^{4} C_{4} (\frac{2}{3})^{4} = \frac{16}{27}$ .

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