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解析1.76亿中奖概率:428万分之1而非4.4亿分之1
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1.76亿！6月27日晚，体彩诞生首个亿元巨奖。一夜之间，重庆彩民中得1.76亿元巨奖的消息引起了大家的热烈讨论，不少人甚至开始计算1.76亿元巨奖的中奖概率，有说是2142万分之一的，有说是4.4亿分之一的，也有说是428万分之一的，今天我们就来谈一下中奖概率的问题。+ m+ W# t4 X2 o& n b
[b]如何计算一等奖中奖概率？[/b]5 z2 l( ]! Y( X7 b( W3 v6 _
每期摇出的奖号是一组数字，每个数字的出现是有一定的概率的，那么一等奖的中奖概率该如何计算呢？: P ]7 K* E5 v4 M; f* v/ z4 F
以超级大乐透为例，购买者从01—35共35个号码中选取5个号码为 前区号码，并从01-12共12个号码中选取2个号码为后区号码组合为一注彩票进行的基本投注，则一等奖中奖概率为：- j3 }0 f( ~: O
前区号码组合总数C(35,5)=3246321 ^. t% m4 ?+ [4 T5 L6 o
后区号码组合总数C(12,2)=66
, j- g1 o! ]8 Z# I2 R0 Q' [; \& C一等奖中奖概率=1/(324632×66)=1/21425712
! v5 g9 U I/ D: g! n {简单来说，假设某彩民采用包号的方法，对所有前、后区号码组合进行投注，即投注了21425712种不同的号码组合，那肯定有且只有1种组合与当期开奖号码完全相同，也就是说他100%可以中得一等奖；如果彩民仅投注一种号码组合，则一等奖中奖概率为1/21425712。如果投注两种不同的号码组合，那么一等奖的中奖概率自然就增加一倍，以此类推。
o' h! K- r. Y6 D[b]4.4亿分之一的说法是否正确？[/b]% x; N$ ]* w6 F& V2 |* z; G
重庆02818投注站中得的1.76亿元分别来自两张彩票：一张5注单式票并进行了追加和20倍倍投、一张7+2复式追加票，因为尚不能确定这两张票肯定为一人中得，我们这里仅分析20倍投的单式票。从票面信息来看，单式票上的其中1注号码与当期奖号完全相同，因为进行了20倍倍投，所以是中得了20注一等奖，另外1注则来自该复式票。需要说明的是，中奖概率只与前、后区号码组合的数目有关，20倍倍投只是提高了中奖后的奖金，但与所选号码的中奖概率没有任何的关系。即使是倍投99倍，但中得一等奖的难度并不会随之提高为原先的99倍，所以4.4亿分之一，即1/(21425712×21)的说法是不对的。: V! ~) f# @4 _: W/ F1 d0 \ {* S6 @
[b]428万分之一如何得来？[/b]
# b# Y, P% A: v, r6 V在这张单式票中，该彩民共选了5注不同的号码，因此5注号码的总中奖概率=5×1/21425712，即该张彩票的中奖概率为428万分之一。1 `+ E& K; g* W" \, A( Z
[b]中奖概率低仍受热捧 原因何在？[/b]" M. T2 |, t( h2 B7 b, Y# v$ @5 ^
仅从中奖概率来看，中得一等奖的机会是很小的，但是超级大乐透仍然受到了很多彩民的热捧，因为这种全国联网大盘玩法有巨额奖池的保障，一等奖奖金十分可观，这从全国动辄中出的千万元以上大奖可见一斑。0 ^( D" l5 K& G9 R( B* D
[b]常见误区：超级大乐透不易中[/b]
5 X$ I# @& `4 w& |# T不少彩民反映超级大乐透不易中，其实这是一个认识上的误区，同样我们从中奖概率的角度来进行分析，仅以八等奖为例。 |
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