Five individuals, including a and b, take seats around a circular table in a completely random fashion. suppose the seats are nu
mbered 1, . . . , 5. let x = a's seat number and y = b's seat number. if a sends a written message around the table to b in the direction in which they are closest, how many individuals (including a and b.would you expect to handle the message?
Will use A and B in place of a and b for clarity. Let x=number of individuals away from A, including A & B
Without loss of generality, assume A is seated in seat #1.
Then B is seated at 2,3,4,5 with equal probability. Half of the time B is seated at 2 or 5, each of which is next to A, therefore x=2 The other half of the time B is seated at 3 or 4, each of which is separated from A by one seat, then x=3.
The expected number of individuals E[X]=sum (x*P(x)) =2*(1/2)+3(1/2) =2.5
So the expected number of individuals to handle the message is 2.5.
