There is a bus with 100 labelled seats (labelled from 1 to 100). There are 100 persons standing in a queue. Persons are also labelled from 1 to 100.
People board on the bus in sequence from 1 to n. The rule is, if the person ‘i’ boards the bus, he checks if seat ‘i’ is empty. If it is empty, he sits there, else he randomly picks an empty seat and sits there. Given that 1st person picks seat randomly, find the probability that 100th person sits on his place i.e. 100th seat.
As the first person has taken the seat randomly, this means the 1st set is vacant. After that, all the passengers will take seat according to their sequence except the seat taken by the 1st person. So, at last, there will be one person left i.e. the 99th person that has the choice of taking the seat from either of the remaining two seats i.e. 100th seat or the other one. On the basis of this, the 100th person will get the seat and the probability of choosing a seat from the 2 seats is 1/2.
- Puzzle 78 | The lost bus Number
- Puzzle 24 | (10 Coins Puzzle)
- Puzzle 27 | (Hourglasses Puzzle)
- Puzzle 28 | (Newspaper Puzzle)
- Puzzle 29 | (Car Wheel Puzzle)
- Puzzle 31 | (Minimum cut Puzzle)
- Puzzle 33 | ( Rs 500 Note Puzzle )
- Puzzle 34 | (Prisoner and Policeman Puzzle)
- Puzzle 36 | (Matchstick Puzzle)
- Puzzle 38 | (Tic Tac Toe Puzzle)
- Puzzle 39 | (100 coins puzzle)
- Puzzle 51| Cheryl’s Birthday Puzzle and Solution
- Puzzle 81 | 100 people in a circle with gun puzzle
- Puzzle 85 | Chain Link Puzzle
- Puzzle | Elevator Puzzle
- Puzzle | 3 Priests and 3 devils Puzzle
- Puzzle | Man fell in well Puzzle
- Puzzle 15 | (Camel and Banana Puzzle)
- Puzzle 1 | (How to Measure 45 minutes using two identical wires?)
- Puzzle 2 | (Find ages of daughters)
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.