there are n people on a round table. one of the them is the head and he plans to make another person from the rest the new head. he has a coin. he flips the coin. if he gets a head he gives the coin to the person to his left and if he gets a tail he gives the coin to the person to his right. anyone who receives the coin can no longer become the head. the person who receives the coin repeats the similar procedure. when there is only one person remaining who has not received the coin, he becomes the head. what is the probability of each of the n-1 people becoming a head.
for n = 3, 4 we get a uniform probability distribution. how to solve it for higher n?
i have struggled with this for some time but could not solve yet.
it seems you are having a tough time solving this! i could not find the solution on google.
approach that i was using:
let ai be the probability of that the ith person is not selected. summation i:1 to n (1-ai) = 1; a1 = 0; we need another equation to use the fact that the probability of getting a head on a coin flip is 1/2. tried Bayes etc. could not get it. try induction anything else you might like