Library / /93 of 99

, 2018

Combinatorics Difficulty 5.0 AIME, harder Prove it United Kingdom

Rachel and Steven play games of chess. If either wins two consecutive games s/he is declared the champion. The probability that Rachel will win any given game is 0.6. The probability that Steven will win any given game is 0.3. There is a 0.1 probability that any given game is drawn. The probability that neither is the champion after at most three games is $P$ . Find the value of $1000P$ .

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.