There are n items in a line. Items are to be picked one by one and removed.
So after each turn one item is removed and the next item is picked from remaining items.
Constraint is that only first item or last item from the remaining items can be picked with probability 0.5.
The last item remaining will be picked by probability 1.
So what is the probability that kth item is picked at odd number of turn means probability of picking kth item in 1st, 3rd ,5th turn and so on.
For clarification, if n=2, then in first turn either item can be picked with probability 0.5 leaving one item which will be picked in next turn.
if n>2, second item can't be picked in first turn, it can be picked in second turn or more turns.