f6M1數學題一問?10點

wai1994926

2011-09-26 3:00 am

Ma Lin plays against Chen Qi in the final of table -tennis tournament,the person who wins three games first will be champion of tournament,players perform independently from game to game and chance that Ma Lin wins a game is 0.6,find expected number of game to be played in final

回答 (1)

用戶2053

2011-09-26 7:59 am

✔ 最佳答案

Expected number of game to be played in final
=3 * P(Ma Lin wins all 3 games) +
3 * P(Chen Qi wins all 3 games)
+
4 * P(Ma Lin wins 2 games in the first 3 games and wins the last game) +
4 * P(Chen Qi wins 2 games in the first 3 games and wins the last game)
+
5 * P(Ma Lin wins 2 games in the first 4 games and wins the last game) +
5 * P(Chen Qi wins 2 games in the first 4 games and wins the last game)
=3 * 0.6³ + 3 * 0.4³
+
4 * (3C2 * 0.6² * 0.4) * 0.6 + 4 * (3C2 * 0.4² * 0.6) * 0.4
+
5 * (4C2 * 0.6² * 0.4²) * 0.6 + 5 * (4C2 * 0.4² * 0.6²) * 0.4
=0.84
+
1.4976
+
1.728=

4.0656

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