Problem A. 381. (October 2005)
A. 381. A die of n faces is rolled until each of the n possible outcomes is obtained at least once. What is the expected value of the number of rolls needed?
Deadline expired on November 15, 2005.
Sketch of solution. It is well-known that the expected number of required experiments to reproduce an event of probability p is exactly 1/p.
If we have k different results of the possible n, we expect another n/(n-k) experiments to produce a new result.
The excpected number of all experiments together is .
26 students sent a solution. 5 points: Balambér Dávid, Csóka Győző, Dücső Márton, Erdélyi Márton, Fischer Richárd, Gyenizse Gergő, Hujter Bálint, Jankó Zsuzsanna, Kisfaludi-Bak Sándor, Kónya 495 Gábor, Korándi Dániel, Nagy 224 Csaba, Nagy 317 Péter, Nagy Gergely Gábor, Paulin Roland, Radnai András, Szűcs Gergely, Tomon István, Udvari Balázs. 4 points: Ureczky Bálint. 3 points: 1 student. 2 points: 1 student. 0 point: 4 students.