Convergence in probability and convergence in distribution are two different thing. If you are in fact meant to show CID, all you need to do is - for an arbitrary k - show that P(Y_n = k) = 1/2^(k+1) as n goes to infinity, which really shouldn't be that hard.

To show CIP , you need to state what the r.v. Y_n is meant to converge to (for example the sample mean converging to the population mean).