Hi Folks, Its long time since I posted here. Any ways thought its time to recharge my grey cells. I came across this puzzle some time back. Liked it, solved it. However, after solving it felt like extending it. Now without holding you back, let me go to the puzzle. Later I will add my extensions to it.
FYI: This puzzle is not my invention, I have taken it from Michael H. Pryor site.
"a line of 100 airline passengers is waiting to board a plane. they each hold a ticket to one of the 100 seats on that flight. (for convenience, let's say that the nth passenger in line has a ticket for the seat number n.)
unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. all of the other passengers are quite normal, 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.
Now comes my extension to it
Lets say the number of crazy guys on the plane is n and the number of seats (and hence the number of people who can board the plane) is N.
What will the probability that the last person (Nth) boarding the plane will get to sit in his seat(#N).
i) n=1 and N=100. (Same as above)
ii) n=1 and N>100.
iii) 1< n="100.
Now I could have put it in more beautiful way as was in the initial statement. I am lazy, and if you could figure out the answer for the first part, you will not have any problem in dealing with the above statements.
Please work out, it is necessary for your brain, don't just wait for the solution as I am not going to post it.