Z is dependent on X and Y and so option B).
Why Z is dependent on X ???
- If X happens, then Z will never happen (i.e) if first 2 tosses result as Heads,then there can never be 2 tails in 3 tosses.
- If X doesnot happen, then Z happens if first 2 tosses are TAIL-TAIL and it may or maynot happen if first 2 tosses are HEAD-TAIL or TAIL-HEAD.
So the occurence of Z is greatly influenced by whether X has happened or not.
Why Z is dependent on Y ???
- If first 2 tosses are HEAD-TAIL or TAIL-HEAD, then whether Z will happen or not depends on whether Y has happened or not (i.e) if Y happen Z will happen else Z willnot happen.
So Z is an event whose occurence is greatly influenced by the occurences of both X and Y.
Note : X and Y are independent. EX: If 2 coins are tossed, outcome of 1 st toss has nothing to do with 2 nd toss (i.e) outcome of 2 nd toss is independent of 1 st toss. Similiarly here outcome of first 2 tosses has nothing to do with the outcome of the 3 rd toss.