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+5 votes

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) X and Y are not independent (B) Y and Z are dependent
(C) Y and Z are independent (D) X and Z are independent

asked in Numerical Ability by Veteran (41.9k points)  
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1 Answer

+2 votes
ans should be B

  event X =HH _

 event  Y= _ _T      so X and Y are independent  so option A is out

 event Z = 2T 1 H (any order TTH,THT,HTT)  so if X occurs Z can not occur hence X and Z are dependent events so option D is out

event Z = 2T 1 H ( TTH(event Y is not possible hence Y and Z are dependent) ,THT(event Y is possible) ,HTT (event Y is possible)

 consider  choice C and D the question is asked about 2 (exactly 2) tails occur in 3 tosses now if there is a tail in 3rd toss then we need only one tail in first 2 tosses else we need 2 tails   hence they are dependent on each other
answered by Veteran (44.1k points)  
edited by
Can anyone please elaborate i am finding it difficult to understand.

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