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.
What is the probability that the last (100th) person to board the plane will sit in their proper seat (#100)?
Sunday, February 21, 2010
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The probability is 1/99.
ReplyDelete1/2
ReplyDeleteProbability that 100th person will not sit in his own place is (based on previous persons were not sitting in their own places )
ReplyDelete99/100 * 98/99 * 97/98 * ......* 3/4 * 2/3 * 1/2 *1
=1/100
then probability that he will sit in his correct position is 1-(1/100) => 99/100
correct me if I am wrong..
it's indeed 1/100, but this is the pobability of the last guy sitting in the right sit.
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