19.
公元1651年,法国一位著名的统计学家德梅赫
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo+stretchy%3D%22false%22%3E%28%3C%2Fmo%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmi%3Ee%3C%2Fmi%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmi%3Ee%3C%2Fmi%3E%3Cmi%3Er%3C%2Fmi%3E%3Cmi%3Ee%3C%2Fmi%3E%3Cmo+stretchy%3D%22false%22%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
向另一位著名的数学家帕斯卡
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo+stretchy%3D%22false%22%3E%28%3C%2Fmo%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E.%3C%2Fmo%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmi%3Es%3C%2Fmi%3E%3Cmi%3Ec%3C%2Fmi%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmi%3El%3C%2Fmi%3E%3Cmo+stretchy%3D%22false%22%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
提请了一个问题,帕斯卡和费马
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo+stretchy%3D%22false%22%3E%28%3C%2Fmo%3E%3Cmi%3EF%3C%2Fmi%3E%3Cmi%3Ee%3C%2Fmi%3E%3Cmi%3Er%3C%2Fmi%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmi%3Et%3C%2Fmi%3E%3Cmo+stretchy%3D%22false%22%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
讨论了这个问题,后来惠更斯
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo+stretchy%3D%22false%22%3E%28%3C%2Fmo%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E.%3C%2Fmo%3E%3Cmi%3EH%3C%2Fmi%3E%3Cmi%3Eu%3C%2Fmi%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmi%3Eg%3C%2Fmi%3E%3Cmi%3Ee%3C%2Fmi%3E%3Cmi%3En%3C%2Fmi%3E%3Cmi%3Es%3C%2Fmi%3E%3Cmo+stretchy%3D%22false%22%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
也加入了讨论,这三位当时全欧洲乃至全世界最优秀的科学家都给出了正确的解答该问题如下:设两名赌徒约定谁先赢
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmo%3E%E2%88%88%3C%2Fmo%3E%3Cmsup%3E%3Cmi%3EN%3C%2Fmi%3E%3Cmo%3E%2A%3C%2Fmo%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
局,谁便赢得全部赌注
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmath%3E)
元.每局甲赢的概率为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ep%3C%2Fmi%3E%3Cmo+stretchy%3D%22false%22%3E%28%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmi%3Ep%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo+stretchy%3D%22false%22%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,乙赢的概率为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmi%3Ep%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,且每局赌博相互独立.在甲赢了
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo+stretchy%3D%22false%22%3E%28%3C%2Fmo%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmo+stretchy%3D%22false%22%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
局,乙赢了
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3En%3C%2Fmi%3E%3Cmo+stretchy%3D%22false%22%3E%28%3C%2Fmo%3E%3Cmi%3En%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmo+stretchy%3D%22false%22%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
局时,赌博意外终止赌注该怎么分才合理?这三位数学家给出的答案是:如果出现无人先赢
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ek%3C%2Fmi%3E%3C%2Fmath%3E)
局则赌博意外终止的情况,甲、乙便按照赌博再继续进行下去各自赢得全部赌注的概率之比
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3E%E7%94%B2%3C%2Fmi%3E%3C%2Fmsub%3E%3Cmo%3E%EF%BC%9A%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3E%E4%B9%99%3C%2Fmi%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
分配赌注.