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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 three tosses. Based on the above information, which one of the following statements is TRUE?

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 three tosses. Based on the above information, which one of the following statements is TRUE? Correct Answer Y and Z are dependent

X be the event that head occurs in each of the first two tosses:

X = {HHT, HHH}

Y be the event that a tail occurs on the third toss:

Y = {HHT, HTT, TTT, THT}

Z be the event that two tails occur in three tosses:

Z = {TTH, THT, HTT}

 ∴ both y and z are dependent.

X is the event that the head occurs in each of the first two tosses and Y is the event that a tail occurs on the third toss. So X and Y are independent.

Z is the event that two tails occur in three tosses and Y is the event that a tail occurs on the third toss. Event {TTH} is not possible. So Y and Z are dependent.

X is the event that the head occurs in each of the first two tosses and Z is the event that two tails occur in three tosses. So if X occurs Z can not occur hence X and Z are dependent.

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