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A先,B后 P(A) = 1/2 + //A直接取胜 1/2 * 1/2 * 1/2 + // A1失败B1失败A2取胜 1/2 * 1/2 * 1/2 * 1/2 *1/2 + //A1失败B1失败A2失败B2失败A3取胜 ... p = 1/2 + (1/2)^3 + (1/2)^5 + (1/2)^7 + ... 等比数列求和 p = 1/2 * (1 - (1/4)^n) / (1 - 1/4) = 2/3 P(B) = 1/2 * 1/2 + // A1失败B1取胜 1/2 * 1/2 * 1/2 * 1/2 + // A1失败B1失败A2失败B2取胜 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 + //A1失败B1失败A2失败B2失败A3失败B3取胜、 ... p = (1/2)^2 + (1/2)^4 + (1/2)^6 + .. p = 1/4 * (1 - (1/4)^n) / (1 - 1/4)
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