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 $2/3$.

wiseowl Oct 16, 2023

#1**+1 **

Look at https://web2.0calc.com/questions/probability-problem_24#r2. Use the same method, suitably modifying the numbers.

Alan Oct 17, 2023

#2**0 **

__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 $(1/3) \cdot (1/3) = 1/9$.__

YusiChahal Oct 17, 2023