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A student walked into a room where he found N pieces of wire. After finding the 2N ends, he casually joined these ends together in pairs until there were no loose ends left. In every turn, he selected one of the unjoined ends with equal probability, and then another unjoined end with equal probability, and then tied the two ends together. Another student found the pile of loops and decided to count how many there are. She reasons that there could be anything from one long loop to N separate loops. What is the expected number of loops if there were five wires in the room?

A student walked into a room where he found N pieces of wire. After finding the 2N ends, he casually joined these ends together in pairs until there were no loose ends left. In every turn, he selected one of the unjoined ends with equal probability, and then another unjoined end with equal probability, and then tied the two ends together. Another student found the pile of loops and decided to count how many there are. She reasons that there could be anything from one long loop to N separate loops. What is the expected number of loops if there were five wires in the room?

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 33E: Find the probability of each event. Drawing 5 orange cubes from a bowl containing 5 orange cubes and...
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A student walked into a room where he found N pieces of wire. After finding the 2N ends, he casually joined these ends together in pairs until there were no loose ends left. In every turn, he selected one of the unjoined ends with equal probability, and then another unjoined end with equal probability, and then tied the two ends together. Another student found the pile of loops and decided to count how many there are. She reasons that there could be anything from one long loop to N separate loops. What is the expected number of loops if there were five wires in the room?
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