Probability of getting the seat..
Lucy was the first to board her flight to Delhi. She forgot her seat number and picks a random seat for herself. After this every single person who gets on the flight sits on his/her seat if it's available or sits on whichever seat is available. Mark is the last to enter the flight and at the moment 99/100 seats were occupied.
What is the probability Mark got to sit in his seat?
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Consider a person who is sitting in a random available seat (i.e. either Lucy, or someone whose assigned seat is taken). Whether or not Mark will sit in his assigned seat is decided when one of two things happens: such a person sits in Mark's seat, or such a person sits in Lucy's original seat. In the first case, Mark will not sit in his seat; in the second case, everyone after that person, including Mark, will sit in their assigned seat.
These two cases are equally likely to happen, so the probability that Mark sits in his seat is 1 / 2 .