Probability problem of the day

Fantastic probability problem – as told by a genius colleague!

100 patient people are standing in line waiting to get on a plane. All of them have their tickets – except the first person, who has left theirs at home. They board the plane in the order in which they have lined up.

The first person boards the plane, and since they don’t know which seat is theirs, they choose any seat. There are exactly 100 seats, so they have a 1/100 chance of getting their own seat.

The next person boards the plane, and if the first person is sitting in their seat, they randomly choose another seat. The person after that boards the plane, and if their seat is already taken, they also choose another seat.

When the final person boards the plane, what is the probability that they will be sitting in their own seat as assigned to them on their ticket?

Think about it…then give it to your maths classes!

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