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Sam is holding two lengths of rope by their mid-points. Pat chooses two of the loose ends at random and ties them together.

What is the probability that Sam now holds one untied length of rope and one tied loop of rope?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

*This problem is taken from the UKMT Mathematical Challenges.**View the archive of all weekly problems grouped by curriculum topic*

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