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Exactly one clears two-thirds

EasyProbabilityRandom Variables~3m

X1,X2,X3X_1, X_2, X_3 are independent uniform on [0,1][0,1]. What is the probability that exactly one of the three exceeds 23\tfrac23? (to 3 decimals)

Show hints (2)+
  1. Each variable exceeds 2/3 with probability 1/3 - it's Binomial(3, 1/3).
  2. 'Exactly one' needs the C(3,1) factor: 3·(1/3)·(2/3)².

Answer

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0.444 (± 0.005)

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