Three points, X 1 , X 2 , and X 3 , are chosen at random in the interval (0, a) A second set of three points, Y 1 , Y 2 , and Y 3 , are chosen at random in the interval (0, b) Let A be the event that X 2 is between X 1 and X 3 Let B be the event that Y 1 Y 2 Y 3 Find P(A B) ...

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Three points, X 1 , X 2 , and X 3 , are chosen at random in

Question:

Three points, X₁, X₂, and X₃, are chosen at random in the interval (0, a). A second set of three points, Y₁, Y₂, and Y₃, are chosen at random in the interval (0, b). Let A be the event that X₂ is between X₁ and X₃. Let B be the event that Y₁ < Y₂ < Y₃. Find P(A ∩ B).