完本神战

Appendix（第1页）

Appendix

&oquestionsposed

Chapter2:Withfairdigeightorteheevennumberis12，andtheultipleofsixis18or110respectively。Therespeultipleofthreeare14（twoi），whichgivesindependend310，whiot。

Chapter6:Intheoneypuzzle，youshouldaimtobank￡12，000atyourfirstchoice。Ifitworks，youhopetobank￡3，000fails，youmusttryfor￡15，000ime。Youroverallwinningceis（612）*（1011）+（612）*（411）=84132=711，whichishigherthaactic。

In46similarpames，theimesaSpadearises，youmakeaof50chips;theother37times，youlosetheextrastake。Ifyoustayinfor12chipsorfewer，you’llbeaheade，butifyouhavetopay13ore，you’llexpeorethanyougain。

Chapter7:Theiscarriageis1in　m，theceofaDown’sbabyis1in　n，both　mand　nlargeandm＞ify＞x+nm。

SupposeAerCeliahas　nsohy。IfBettyisnotacarrier，allCelia’ssoobehealthy;ifBettyisacarrier，theceCeliawillnotbeacarrier（andhenceallhersohy）is12，andthecesheisacarrier，buthelessallhersohy，is（12）n+1。SotheposterioroddsofBettybeingacarrier，aftertheinformationaboutallAhyhepriorodds（i。e。thoseputedusiionaboutAhybrothers），multipliedbyallthesefactorsoftheform（12+（12）n+1）fromhersisters。vertthisfigureintotheprobabilitythatBettyisacarrier，aofindtheeisacarrier。

Chapter8:Intherandomizedresponseexamples，supposetheproportionofsmokersis　x，andallahful。Thecase，theoverallproportionof‘Agree’answersis0。8x+0。2（1-x）;equatethisto13，solvetofind　x=29。Inthesedcase，theproportionof‘Yes’answersis0。8x+0。22;settio13gives　x=724。

Chapter9:Let　xbethemeahrowstogetHH。TogetthefirstHtakestwothrows，e。Afterthis，weohrow;ahen，halfthetimewemustbeginagain。So　x=2+1+（x2），hence　x=6。

&e，ifyouropposHHH，youshouldchooseTHH，andyceis78;ifshepicksHHT，agaiHH，andwin34ofthetime;toherHTH，respondHHT，againstTHH，useTTH–inboththesecases，expe23ofthetime。SymmetryleadstothebestchoistTTT，TTH，THT，andHTT。