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Omni-MATH / Let A,B,C, and D be points randomly selected independently and uniformly within the unit square. What is the probability that the six lines …,and(CD)¯ all have positive slope?

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problem

Let A,B,CA, B, C, and DD be points randomly selected independently and uniformly within the unit square. What is the probability that the six lines \overline{A B}, \overline{A C}, \overline{A D}, \overline{B C}, \overline{B D},andCD¯, and \overline{C D} all have positive slope?
Plain-text mathematical notation (without MathML)
Let A,B,C, and D be points randomly selected independently and uniformly within the unit square. What is the probability that the six lines \overline{A B}, \overline{A C}, \overline{A D}, \overline{B C}, \overline{B D},and(CD)¯ all have positive slope?
Original LaTeX notation
Let $A, B, C$, and $D$ be points randomly selected independently and uniformly within the unit square. What is the probability that the six lines \overline{A B}, \overline{A C}, \overline{A D}, \overline{B C}, \overline{B D}$, and \overline{C D}$ all have positive slope?

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