江苏省扬州中学2016届高三上学期10月月考试题 数学（理） Word版含答案

②证明：设乙每一局获胜的概率为q，则p?q?1,0?q?记在甲最终获胜的概率为Pn，则

nnnn2nnnPn?pn?1?pCnpq?pCpq?...?pCpq?1n?22n1． 2?pn?1?1?Cnn?1q?Cnn?2q?...?Cq2n2nn?

nn2nnn?1n?12n?1n?1Pn?Pn?1?pn?11?Cn?pn?21?Cn?1q?Cn?2q?...?C2nq?2q?Cn?3q?...?C2n?2qnn2nn?pn?11?Cn?1q?Cn?2q?...?C2nq?pn?1所以，

n?12n?13n?1n?2?q?Cn?2q?Cn?3q?...?C2n?2q?????1?C???nn?1n2nnq?Cn?2q?...?C2nq?????1?q??1?Cq?Cq?...?Cq?????1?Cq?Cq?...?Cq???n?1n?2n?12n?3n?12n?2n?1n?1n?2n?12n?3n?12n?2n?1?nn?12nn?1?pn?1(1?1)?q(Cn?1?Cn?2?1)?q(Cn?2?Cn?3?1)nn?1n?1n?1n?1n?1n?2n?1?...?qn(C2(C2C2n?2n?C2n?1?C2n)?qn?2?C2n?1)?qn?1n?1n?2n?1?pn?1?qn?1(C2C2n?2n?2?C2n?1)?q

n?1nn?1n?1nn?pn?1qn?1qC2q2qC2n?2?C2n?1?pn?1?C2n?1n?pn?1qn?1C2n?1?2q?1??0??????所以Pn?Pn?1

即总局数越多，甲获胜的可能性越大（即甲获胜的概率越大）． ???10分