HKALAM 2 1992.

2009-04-13 6:14 am

a plays B in the final of a table-tennis tournament.The match consists of five games.In each game, the probability that A WINS is 0.3 and the probability that B wins is 0.7.Find the probability that A become the champion.

The rules.
Whoever wins three games before the other wins two becomes the champion.If both win two games, they continue to play and the one first wins two more games than the other becomes the champion.

I think the answer is
0.3^(3)+0.3^3X0.7X3C1+(0.3^2X0.7^2X4C2)X(0.3^2+0.3^3X0.7X3C1)

I THINK THIS PART MAY BE INCORRECT.

(0.3^2+0.3^3X0.7X3C1)

HOW TO CALCULATE? ANSWER IS:0.1247

回答 (1)

用戶2053

2009-04-13 7:10 am

✔ 最佳答案

Yes! It is incorrect as you think.
The correct calculate of this part is :
0.3^(3)+0.3^3X0.7X3C1+(0.3^2X0.7^2X4C2)X[0.3^2 +
(2*0.3*0.7)(0.3^2) + (2*0.3*0.7)^2 * (0.3^2) + (2*0.3*0.7)^3 * (0.3^2) + ...]
= 0.3^(3)+0.3^3X0.7X3C1+(0.3^2X0.7^2X4C2)x
0.3^2/(1- 2*0.3*0.7)
= 0.1248

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