All three land in the same half

X1,X2,X3X_1, X_2, X_3 are independent uniform on [0,1][0,1]. What is the probability that all three fall in the same half of the interval - i.e. all three are below 12\tfrac12, or all three are above 12\tfrac12? (to 3 decimals)

Show hints (2)+
  1. 'Same half' can happen two ways - all below 1/2, or all above.
  2. Each way is (1/2)^3; add the disjoint cases.

Answer

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0.25

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Asked at: Game-Based Aptitude, ETF Market-Making

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