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Appendix
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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+n
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.
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