Directions: Carry Two Marks Each.

A coin is tossed thrice. Let X be the event that head occurs in each of the first two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occur in the three tosses. Based on the above information, which of the following statements is TRUE?

For a coin tossed 3 times, Let X be the event that head occurs in each of the first two tosses. So, set X = {HHT, HHH} Now, let Y be the event that a tails occurs on the third toss. Statement implies first two must be heads for tails in third toss. Set Y = {HHT} It implies event Y is dependent on event X. Now, let Z be the event that two tails occur in the three tosses. So, set Z = {TTH, TTT, THT, HTT} Now, we can see that event X and event Z are independent as their sets have no common occurrence.