You are the bus driver. At your first stop, you pick up 29 people. On your second stop, 18 of those 29 people get off, and at the same time 10 new passengers arrive. At your next stop, 3 of those 10 passengers get off, and 13 new passengers come on. On your fourth stop 4 of the remaining 10 passengers get off, 6 of those new 13 passengers get off as well, then 17 new passengers get on. What is the color of the bus driver’s eyes?
I’m in an elevator with two other people. When it reaches the first floor, one person gets out and six get in. When it reaches the second floor, three people get out and twelve get in. At the third floor, five leave and nine enter. It rises to the fourth floor, one person gets on and the doors close. Suddenly, the elevator cable snaps and the car smashes to the ground. No one survives the fall, yet I’m alive and know exactly how many people go on and off the elevator at every floor. How is this possible?
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.
If a piece of rope was tightly wrapped around the earth and you added 3 feet to its length, how high could you uniformly raise it from the earth’s surface?