Each one of n persons, indexed by 1,2,…,n, has a clean hat and throws it into...
Each one of n persons, indexed by 1,2,…,n, has a clean hat and throws it into a box. The persons then pick hats from the box, at random. Every assignment of the hats to the persons is equally likely. In an equivalent model, each person picks a hat, one at a time, in the order of their index, with each one of the remaining hats being equally likely to be picked. Find the probability of the following events.
(You need to answer all 5 questions before you can submit.)
a. Every person gets his or her own hat back.
b. Each one of persons 1,…,m gets his or her own hat back, where 1≤m≤n.
c. Each one of persons 1,…,m gets back a hat belonging to one of the last m persons (persons n−m+1,…,n), where 1≤m≤n.
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Each one of n persons, indexed by 1,2,…,n, has a clean hat and
throws it into...
1. The hats of n persons are so that every assignment of the hats to the...
1. The hats of n persons are so that every assignment of the hats to the persons is equally likely). What is the probability thrown into a box. The persons then pick up their hats at random (i.e., that (a) every person gets his or her hat back? (b) the first m persons who picked hats get their own hats back? (c) everyone among the first m persons to pick up the hats gets back a hat belonging to one...
1. p people, each wearing a different hat, throw their hats into the ring. They all have second t...
1. p people, each wearing a different hat, throw their hats into the ring. They all have second thoughts, run into the ring, and start randomly grabbing as many hats as they can, without regard to ownership, some obtaining many hats, others emerging from the chaos hatless. Compute the probability that every person who manages to grab at least one hat manages to retrieve not only their own hat but also one or more hats that do not belong to...
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Please help me :)
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write clearly please if you’re hand writing.
can’t understand answers sometimes
thanks
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1. The hats of n persons are so that every assignment of the hats to the persons is equally likely). What is the probability thrown into a box. The persons then pick up their hats at random (i.e., that (a) every person gets his or her hat back? (b) the first m persons who picked hats get their own hats back? (c) everyone among the first m persons to pick up the hats gets back a hat belonging to one...
1. p people, each wearing a different hat, throw their hats into the ring. They all have second thoughts, run into the ring, and start randomly grabbing as many hats as they can, without regard to ownership, some obtaining many hats, others emerging from the chaos hatless. Compute the probability that every person who manages to grab at least one hat manages to retrieve not only their own hat but also one or more hats that do not belong to...
Exercise 1.15. Assume that the numbers 1,2, n are randomly given to players labeled 1,2,...,n. Initially, player 1 and player 2 compare their numbers. The one with the largest number wins and compares her number with player 3, and so on. Find the probability that player 1 wins m times. Hint: Use that, for every subset of numbers chosen uniformly at random, all the possible permutations of these numbers are equally likely. 1nl and define
Please help me :)
#5. Ms. Lee is famous for her parties in the Seoul area. In each four-year administration she throws k parties, set m tables at each party and seats n people at each table. She makes a list of mn influential people at the start of the four year period and invites them to every party. Her tables are all distinct from cach other (teak, oak, cherry, etc.) and k S m. It is rumored that her...
write clearly please if you’re hand writing.
can’t understand answers sometimes
thanks
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