GATE CSE
First time here? Checkout the FAQ!
x
+5 votes
337 views

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 (43.7k points)  
retagged by | 337 views

2 Answers

+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 (45k points)  
edited by
Can anyone please elaborate i am finding it difficult to understand.
+1 vote

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.

answered by Loyal (3.6k points)  


Top Users Sep 2017
  1. Habibkhan

    6334 Points

  2. Warrior

    2202 Points

  3. Arjun

    2150 Points

  4. nikunj

    1980 Points

  5. manu00x

    1726 Points

  6. SiddharthMahapatra

    1718 Points

  7. Bikram

    1706 Points

  8. makhdoom ghaya

    1650 Points

  9. A_i_$_h

    1518 Points

  10. rishu_darkshadow

    1512 Points


25,979 questions
33,554 answers
79,347 comments
31,011 users