At the Theatre
10
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Categories: Logic, Mathematical
 
Kiki's class (which has 99 students in all) is going on a picnic to see the movie "The Chronicles of Narnia: Prince Caspian". At the theater (which incidentally has a 100 seats) the teacher asks the students to form a queue as per the ticket number held by them. The tickets are numbered from 1 to 100 such that Nth person in line holds a ticket for seat number N. However, the first child in the line is a naughty one. He ignores the seat number on his ticket and picks a random seat to sit. All the other persons are quite normal, and they go to their proper seat. If it is occupied, then they find a free seat to sit in, at random. What is the probability that the last person to enter the theater will sit in his/her proper seat i.e. seat number 100?
 
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