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The numbers $x_1,$ $x_2,$ $x_3,$ $x_4$ are chosen at random in the interval $[0,1].$  Let $I$ be the interval between $x_1$ and $x_2,$ and let $J$ be the interval between $x_3$ and $x_4.$  Find the probability that intervals $I$ and $J$ both contain the number $2/3$.

 Oct 16, 2023
 #1
avatar+33595 
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Look at https://web2.0calc.com/questions/probability-problem_24#r2.  Use the same method, suitably modifying the numbers.

 Oct 17, 2023
 #2
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The probability that the interval I contains $2/3$ is $1/3.$ The probability that interval J also contains $2/3$ is $1/3.$ So, the probability that both I and J contain $2/3$ is $(1/3) \cdot (1/3) = 1/9$.

 
 Oct 17, 2023
edited by YusiChahal  Oct 17, 2023

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