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Greetings at a Party

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

 

Puzzle ID:#3406
Fun:*** (2.36)
Difficulty:*** (2.67)
Category:Probability
Submitted By:cathalmccabe***
Corrected By:Winner4600

 

 

 



10 people are gathering in a room. Each person is meeting every other person. There are three types of greetings: a quick hello, which will take 40 seconds; a short chat, which will take 1 and a half minutes; or a longer greeting, which will take 2 minutes. Each greeting is completely random, and duration depends on the longer person. What is the probability that this gathering will take 1/2 an hour or less?
Assume no time loss between meetings with different people.




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