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Tying the Knot

A civilization in a far off land has an unusual custom about marriage. The leader holds six pieces of string in her fist so that six pieces stick out of the top and six pieces stick out of the bottom (and you can't see the middle of the string). The chief tests the potential for marriage by involving the couple in a knot tying ceremony. Each knot is formed by tying the ends of two pieces of string. The ceremony includes the following events:

• the first partner ties three different knots using the top parts of all six pieces of string,
• the second partner ties three different knots using the bottom parts of all six pieces of string,
• the chief releases her fist to show all of the strings and shows the number of loops that were created

If the chief, shows exactly one loop, then the couple can be married.

What are the chances that a couple can get married under this custom? Design a simulation that will help you answer this question. Explain your experimental design and results.

 Extensions

Determine the theoretical probability that two people can get married under this custom. Explain your reasoning.

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