IOM 2021, Блиц — Задача 11

The Blitz-contest of IOM-2021

Условие

Hazel the mouse wants to get out of a maze. His starting point is room A. Whenever he is in a room, he runs out into one of the outgoing passageways; each time he chooses each passageway with equal probability. (He has 66 options in room A and 44 options in room B.) On the map of the maze below, next to each passageway, it is written how long (in minutes) it takes for Hazel to run through it. What is the expected time in minutes for Hazel to get out of the maze?

Map of the maze: two rooms drawn as circles, B on the left and A on the right, and the Exit at the top. Passageways are labelled with their times: 6 (from B to the Exit), 4 (from B to A), 3 (from A to the Exit), 2 (a loop from B back to B), 5 (a loop from A back to A) and 7 (a loop from A back to A).

If the answer is a fraction, it can be entered either as a decimal fraction or as a ratio “r/sr/s”. Rounding is not allowed.

Отговори

Решение

Оригинал в Архива: iom-2021-blitz-tasks-eng.pdf · официални решения: iom-2021-blitz-answers-eng.pdf