math

A Drunk Person at the Theater

There are 𝑛 people in line, indexed by 𝑖=1,…,𝑛, to enter a theater with 𝑛 seats one by one. However, the first person (𝑖=1) in the line is drunk. This person has lost her ticket and decides to take a random seat instead of her assigned seat. That is, the drunk person decides to take any one of the seats 1 to 𝑛 with equal probability. Every other person 𝑖=2,…,𝑛 that enters afterwards is sober and will take his assigned seat (seat 𝑖) unless his seat 𝑖 is already taken, in which case he will take a random seat chosen uniformly from the remaining seats.

Suppose that 𝑛=3. What is the probability that person 2 takes seat 2?

Suppose that 𝑛=5. What is the probability that person 3 takes seat 3?

  1. 👍 11
  2. 👎 2
  3. 👁 2,854
  1. a)2/3
    b)1/5

    1. 👍 1
    2. 👎 13
  2. a) 1-P(drunk person sits in seat 2)
    b) 1-P(drunk person sits in seat 3 OR (drunk person sits in seat 2 AND person 2 sits in seat 3))

    1. 👍 5
    2. 👎 0
  3. i dont know answer is this correct or not

    a) 2/3
    b) 3/4

    1. 👍 3
    2. 👎 0
  4. b) 4/5

    1. 👍 0
    2. 👎 1

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