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Omni-MATH / Five equally skilled tennis players named Allen, Bob, Catheryn, David, and Evan…

Problem

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problem

Five equally skilled tennis players named Allen, Bob, Catheryn, David, and Evan play in a round robin tournament, such that each pair of people play exactly once, and there are no ties. In each of the ten games, the two players both have a 50%50 \% chance of winning, and the results of the games are independent. Compute the probability that there exist four distinct players P1,P2,P3,P4P_{1}, P_{2}, P_{3}, P_{4} such that PiP_{i} beats Pi+1P_{i+1} for i=1,2,3,4i=1,2,3,4. (We denote P5=P1P_{5}=P_{1} ).
Plain-text mathematical notation (without MathML)
Five equally skilled tennis players named Allen, Bob, Catheryn, David, and Evan play in a round robin tournament, such that each pair of people play exactly once, and there are no ties. In each of the ten games, the two players both have a 50% chance of winning, and the results of the games are independent. Compute the probability that there exist four distinct players P₁,P₂,P₃,P₄ such that P_(i) beats P_(i+1) for i=1,2,3,4. (We denote P₅=P₁ ).
Original LaTeX notation
Five equally skilled tennis players named Allen, Bob, Catheryn, David, and Evan play in a round robin tournament, such that each pair of people play exactly once, and there are no ties. In each of the ten games, the two players both have a $50 \%$ chance of winning, and the results of the games are independent. Compute the probability that there exist four distinct players $P_{1}, P_{2}, P_{3}, P_{4}$ such that $P_{i}$ beats $P_{i+1}$ for $i=1,2,3,4$. (We denote $P_{5}=P_{1}$ ).

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Source and history

task_id
4e033fb8-7dfe-543a-b7c3-c8715f82e293
task_key
test--4e033fb8-7dfe-543a-b7c3-c8715f82e293
task_revision_id
1
config / split
/ test

Official source

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