drunk passenger probability variant?

Question

An aeroplane with 100 seats has  passengers lined up in order, for boarding from seat #1 to #100. However, the first passenger is drunk, and will take any of the seats at random. All other passengers will take their own seat if it is vacant, or else take another seat at random.

What is the probability that the 50th passenger will get seat #50 ?

gianlino · Accepted Answer

Consider seats 1 and 50 up to 100. That's 52 seats

While seating the 49 first passengers exactly one of these seats is taken. Indeed as soon as such is the case all subsequent passengers till 49 will find their seats free.

So one out of these 52 seats is taken when the turn of passenger 50 comes. Hence his seat is taken with probability 1 / 52 and free with probability 51 / 52.

drunk passenger probability variant?

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