A mile from end to end, yet as close to as a friend. A precious commodity, freely given. Seen on the dead and on the living. Found on the rich, poor, short and tall, but shared among children most of all. What is it?
You’re waiting to board your flight at the airport with 99 other passengers, each with an assigned seat. All but one of the passengers will gladly sit in their designated seat. The only exception is Randall, a scoundrel who refuses to follow the rules. When he boards, he will choose a random, unoccupied seat.
If a rule-following passenger finds someone in their spot, they will choose another one at a random from the remaining unoccupied seats.
What is the probability that the last person to board the plane will sit in their proper seat?
The randomness stops as soon as someone else sits in Randall’s assigned seat. The chances of this happening range from 1 out of 99 to 1 out of 1 (when only one seat remains).
Thus, the probability of the last person sitting in their own seat can be calculated as 1/99 plus the sum of 2 to 98 of the formula 1 / n × (n + 1), which works out to 0.5, or 50%.
So there’s a 50% chance the last passenger will sit in their own seat thanks to Randall for screwing up order and procedure when boarding an aircraft.
Mario, from Super Mario Brothers video game by Nintendo. He roams the land searching for the princess and his primary method of getting rid of folks is to stomp on them.
Donald and Regan are married with four children, named Michael, Farley, Solomon and Larry. They just had a baby girl and are picking the name. It’s down to Olivia, Tiffany and Jasmine. Donald’s brother, a piano teacher, tells them only one of the names would be correct. Which name is it?