Compute probability last passenger gets own seat
Problem Description
There are 100 passengers boarding an airplane with 100 seats, numbered 1 to 100. Each passenger i (where 1 ≤ i ≤ 100) holds a ticket for their assigned seat i.
The boarding process unfolds as follows:
- Passenger 1 (P1) is intoxicated and disregards their assigned seat. They choose one of the 100 seats uniformly at random and occupy it.
- For each subsequent passenger
k(from 2 to 100):- If their assigned seat
kis still vacant, they sit in seatk. - Otherwise (if seat
kis already occupied), they choose uniformly at random from all the remaining empty seats and sit in one of those.
- If their assigned seat
Your Task:
Determine the probability that Passenger 100 ends up sitting in their own assigned seat (seat 100). Provide the final probability as a simplified fraction or decimal.
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Compute probability last passenger gets own seat
Problem Description
There are 100 passengers boarding an airplane with 100 seats, numbered 1 to 100. Each passenger i (where 1 ≤ i ≤ 100) holds a ticket for their assigned seat i.
The boarding process unfolds as follows:
- Passenger 1 (P1) is intoxicated and disregards their assigned seat. They choose one of the 100 seats uniformly at random and occupy it.
- For each subsequent passenger
k(from 2 to 100):- If their assigned seat
kis still vacant, they sit in seatk. - Otherwise (if seat
kis already occupied), they choose uniformly at random from all the remaining empty seats and sit in one of those.
- If their assigned seat
Your Task:
Determine the probability that Passenger 100 ends up sitting in their own assigned seat (seat 100). Provide the final probability as a simplified fraction or decimal.