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Beating three others

EasyProbabilityRandom Variables~3m

Let X1,X2,…,X20X_1, X_2, \dots, X_{20} be independent Uniform(0,1)\text{Uniform}(0,1) variables. Compute P[X1>max⁡{X2,X10,X15}]\mathbb{P}\big[X_1 > \max\{X_2, X_{10}, X_{15}\}\big].

Show hints (2)+
  1. The event only involves X1,X2,X10,X15X_1, X_2, X_{10}, X_{15} - four i.i.d. variables.
  2. By symmetry each is equally likely to be the largest.

Answer

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0.25

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Asked at: Jane Street, SIG

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