# Sitting in a bus

There is a bus with 50 labelled seats from 1 to 50. There are also 50 persons labelled from 1 to 50 standing in a queue.

People board on the bus in sequence from 1 to n. The rule is, if a 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 50th person sits on his place i.e. 50th seat.

Once the first person finds a seat, remaining all people will sit in sequence. so, the 49th person can either sit on the seat allocated to 50th person or somewhere else.

Based on where he sits, the last person i.e. 50th person will have 2 options – sit on the 50th seat or somewhere else.

Hence probability is 1/2.

The answer is correct but the explanation not accurate. The remaining people do not necessary sit in sequence!!

Lets go backwards. If there where only 3 seats and the 1st person did not take your seat than the 2nd person can choose between your seat or the 1st person seat so the probability is 1/2.

If there are 4 seats than there are 3 empty seats: yours, 1st person, and the person before the last. so the 2nd person has a probability of 1/3 that he chooses your seat, or 1st person seat, or the person before the last, So if he didn’t choose your seat we come back for the probability of 1/2 for the person before you and so on.

### Your Answer

## More puzzles to try-

### Key, Door, Lock, Room, Switch on

Key, Door, Lock, Room, Switch on Arrange the words given above in a meaningful sequence. A) 4, 2, 1, 5, ...Read More »### You throw away the outside and cook the inside riddle

You throw away the outside and cook the inside. Then you eat the outside and throw away the inside. What ...Read More »### What happens when you throw a blue rock into the yellow sea?

What happens when you throw a blue rock into the yellow sea?Read More »### Maths Puzzle

In a bouquet of flowers, all but two are roses, all but two are tulips, and all but two are ...Read More »### A Man in Elevator

A man who lives on the tenth floor takes the elevator down to the first floor every morning and goes ...Read More »### Dropping eggs

There’s a certain kind of egg about which you wonder: What is the highest floor of a 36-story building from ...Read More »### Dracula died why?

Dracula was out getting a drink but his watch was broken so he died. Why?Read More »### Milk measurement puzzle

There is a person who delivers milk to houses. He has lost some of his measuring utensils. He has left ...Read More »### 3 Dice rolls to get coins Puzzle

You play a game where you are allowed 3 dice rolls. If at any step you decided to end the ...Read More »### Big, Small & absent

It is big on Saturday and Sunday. Small on Tuesday, Wednesday, and Thursday. It is not on Monday or Friday. ...Read More »### What is x?

8 , 6 , 2 = 4 12 , 5 , 8 = 15 13 , 10 , x ...Read More »### Clean bowled one day cricket match

Let’s say that a One Day International Cricket match is going on and every Batsman is getting clean bowled on ...Read More »### What is the chance of flipping heads again?

You have three coins. One always comes up heads, one always comes up tails, and one is just a regular ...Read More »### Hide and Seek

A farmer was playing hide and seek with his wife. His wife hid in their family’s vehicle. How did the ...Read More »### Throwing in the sea puzzle

If you drop a yellow hat in the Red Sea, What does it become?Read More »### Sequence Puzzle

There is this one man who killed his mother, was born before his father and married over 100 women without ...Read More »### Make you smile

It can bring tears to your eyes; breathe new life into the dead, make you smile, and reverse time. It ...Read More »### Can you find the killer?

Sherlock holmes is called upon on a crime scene. A woman has been killed and there are only three suspects ...Read More »### Counting Legs of Animals in zoo Puzzle

A Leopard has four legs, a spider has eight legs and a cricket has six legs. The total number of ...Read More »### Find the Code

During a secret mission, an agent gave the following code to the higher authorities AIM DUE OAT TIE MOD However, ...Read More »