200 students are waiting to enter the auditorium where Belhi University is conducting its annual convocation. Each student has been assigned a seat number (from 1 to 200) and has been requested to seat in their respective seats only. Each student is allowed to enter the auditorium in the order of their seat numbers. Amitabh the rebel, who holds the token for seat #1 always believes in breaking the rules. He will ignore the instructions and randomly occupy a seat. All of the other students are quite obedient, and will go to their proper seat unless it is already occupied. If it is occupied, they will then find a free seat to sit in, at random. What is the probability that the last (200th) student to enter the auditorium will seat in his proper seat (#200)?
Option
(a)1/200
(b)1/100
(c)1/10
(d) 1/2

• ans=1/2.
  when last person enter in the auditorium then there is only one sit is vacant,
  and that sit may be proper or may be wrong both possibility is there,
  so the probability is 1/2.
• 10 years agoHelpfull: Yes(53) No(5)
• d) 1/2 is the answer .
  total cases - 2. (1)amitabh sitting in 200 place (2) or any other place , however he wont sit at his place 1.
  favourable case is - 1 , amitabh not sitting then 200th person sits at his own place , because all others are obedient , so if amitabh sits at 3 for supose then 3rd person calmly goes and sits in amitabh's place without disturbing others order.
• 10 years agoHelpfull: Yes(7) No(7)
• Its A. 1/200 is the answer
• 10 years agoHelpfull: Yes(6) No(12)
• The answer is 1/200..
  Solution :- For 200th student to sit on his seat none of the 199 persons who entered before him should occupy his seat.
  Now, since Amitabh is going to RANDOMLY occupy a seat, so he may or may not seat on his seat.
  So, Proabability that 200th student seats on his seat = P(1st student doesnt seats on 200th seat)*P(2nd student doesnt seats on 200th seat) * P(3rd student doesnt seats on 200th seat).....(so on)
  = (199/200) * (198/199)*(197/198).......*(1/2) = 1/200
• 9 years agoHelpfull: Yes(2) No(2)
• http://www.careerbless.com/qna/discuss.php?questionid=947
• 6 years agoHelpfull: Yes(1) No(0)
• Rochit @ P(1st student doesnt seats on 200th seat) will be 198/200 ? amitabh will not sit in his own place .
  
• 9 years agoHelpfull: Yes(0) No(0)