# 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-

### Genie with c hats

A bunch of men are on an island, A genie comes down and gathers everyone together and places a magical ...Read More »### 13th Floor

Why do you find that most of the buildings are deprived of the 13th floor?Read More »### Arrange in order

Put the following buildings or structures in order of height, from the shortest to the tallest. 1. Shed 2. Skyscraper ...Read More »### A PING-PONG BALL IN A HOLE

Your last good ping-pong ball fell down into a narrow metal pipe imbedded in concrete one foot deep. How can ...Read More »### Which letter replaces the question mark

Which letter replaces the question markRead More »### Funniest Blonde

A blonde put eyeliner on her head. Why?Read More »### What do these things all have in common

What do these things all have in common: Laughter, living well, and a good offense?Read More »### Bones in human body riddle

Which is bigger in quantity and how much: days in a year or bones in an adult human body ?Read More »### Chess board puzzles

We all know that a chess board has 64 squares. This can be completely covered by 32 cardboard rectangles, each ...Read More »### Truck on a bridge riddle

A semi truck weighing exactly 10,000 pounds(Total Weight of truck) gets onto a bridge that is 100 miles long. The ...Read More »### Go on Vacation

Where do fish go on vacation? Where do songbirds go on vacation? Where do zombies go on vacation? Where do ...Read More »### Who am I?

If you say my name, I’ll no longer exist. What am I?Read More »### Magic Squares

There are four sticks of length ‘a’ and four more sticks of length ‘b’. The length of ‘b’ is exactly ...Read More »### James Bond Archer

James Bond is caught up in a mysterious scenario where the evil villain has him blindfolded. He somehow breaks through ...Read More »### How the man got busted puzzle

A man can make perfect counterfeit bills. They look exactly like real ones, they’re made of exactly the same materials, ...Read More »### He has 9 eyes

He has 6 ears, 3 mouths, 9 eyes and 4 noses. What is he?Read More »### Globe Walker puzzle

How many points are there on the globe where, by walking one mile south, then one mile east and then ...Read More »### Make a sentence

Make a sentence consisting of three words that have the whole alphabet.Read More »### Find the next number in the sequence

What are the next three numbers in this series? 4, 6, 12, 18, 30, 42, 60, 72, 102, 108, ?, ...Read More »### Word Ladder

Complete the word ladder in 7 moves by removing one letter in each rung.Read More »