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Tying the Knot

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 

Puzzle ID:#33450
Fun:*** (2.35)
Difficulty:*** (2.8)
Category:Probability
Submitted By:medster99*

 

 

 



There are 6 strings clustered together. One end of each string is at point B (the top), and the other at point A (the bottom). First, two of the ends at point A (randomly) are tied together. Then the two more are tied together, and then the last two. Next, two ends at point B are tied together. Then the two more are tied together, and then the last two.
What is the possibility that all the strings will be tied together in one large loop?

Note: Simplify the answer.


Hint

There are three possible combinations of loop sizes that the strings can form.
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