Sitting in a bus

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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.

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    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.

    bhola99 Expert Answered on 13th August 2020.
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