Damn, this must be one very big bowl of pasta...
You are sitting at a table that contains 'n' number of people and 'd' distance away from the person who initially has the bowl of pasta: what is the probability of being the last person to receive pasta?
The Rules are as follows:
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There is exactly enough pasta for everyone at the table, and every person only takes one serving.
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The person taking a serving of pasta can only pass it directly to the person left or right (50% chance to go either way)
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If a person already received pasta and gets the bowl a second time they do not change the direction the bowl is moving in - the bowl keeps going in one direction until it reaches someone who has yet to take a serving (who then has a 50% chance of passing it back).
Write an equation for the probability of being the last person to receive pasta, the equation should hold for all possible values of 'n' from 2 people to infinity, and all values of 'd' (where 'd' it is measured in minimum number of passes from starting person) from d= 1 to infinity.
Because the equation would be hard to plug in - Once you have the equation, count every variable in the equation as = 1 (example, if 'n' showed up twice and 'd' once in the equation count that as 3), every factorial (!) = 10, and every numerical number = 5 (example, if '2' showed up 3 times in the equation count that as 15). Add all of this up, and plug it in!
The answer is 60.
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1 solution
The final equation is
probability of being last = ( n − d − 1 ) ! ( d − 1 ) ! ( n − 2 ) ! 2 2 − n
there are a total of 5 variables, 5 numbers, and 3 factorials. which is 5 + 25 + 30 = 60