FIFTY CHALLENGING PROBLEMS IN PROBABILITY WITH SOLUTIONS Frederick Mosteller TO MY MOTHER Fifty Challenging Problems in Probability with Solutions EREDERIC Prefer of He Dover Publications, Ine., New York, 1iPtpin was uc fo Anand nemo Cop) "nin. fain ana uae cgay tates Rena, WA Adon ee Ga ba ee gaat eae ser sis Tate essai Bano sae ese ges Preface "his Book conuins 6 probenaalitougs only $0 ars promid. A ‘ove of hm profi rare for er en ner tre ie, sare ‘aes ay ot thallenge you: aly, sc me dc eal thn sl yeu Te yous enna fo len ns net Yeen eens, prong Ate al romck nthe aan of Probl 48 One ef thee probe fran, Wal you be ihe one whe mgs? BOON a, bal Fao hen pra pete ‘Mach of eh Ihave Kae, x2 wl xt mich of my nist én jin, as Do theuth prolong. Throtsh he ena, ¥en Tor it his sees arse ut thal what J have lesrned playing with problems I been ul inser wor, 3 prele,ce eat Thing is The chang poblem cin be ch the eaiaer cokes ustopbisiedlaciion, bes Ht Mts ob Siu oft sear tolutn, orem bus 6 Ue tmply or Fey ‘he anewe, Tn is bok, many ofthe problems ate sy mane ote hard. ery few enjize eal, vt gtson Wika i ogni my eau the peaked ie anette sare T hve orn re cance the chatlerge than sat russel ting te alma een fo Jeans, i @ spel foe aed tet the sete son 20t hive tI ger Rp ot con ni repaenins | have copied er ade ‘Strings approimation forthe Sete: (awe Prbiem UH) and cles uyoxition fot the paral Siu of @ hone aie ce Prone 8) remo at Hd 0 2, Ybih eds Boies of cll fo tel ound a «shih Tm he Sule acon the apr igh cere othe ofa pes cces cheater ef helt prtley wing disused on dx pe Neng ht say be of ele ting ek afr ia the bok, get enone the tr, -Angome wring on pbs in poo vex wes debt nthe ale spat pofsion 42 wee aod probably W._&. Wher and We ook Che amt chance (Hare Pubising Ce, 1958, Replat of th ca {Son mach ei, ant fn OL pric ‘Obs of te pleaes of « putas ihe eppenOsy gis he aur tovnckncaige his dee to FendeTo Rover TK, Rowe 3 fhe reli or WME Fr persuading "pew Suembl th bike; ain rane ‘rota tbe wording has been none y Hs wv. My oll nde nd erin Andren Glesrn, 1-3. Svage, a fotn Dy Wit jet Uenethen the tnt by seupaing alia pets Tor incon, hy testing ctcagexeasions fo some of th slwnon. sa eel ‘Seng to exchange ig for wrong: olay ws abet et cl @ {gation ail. ad converatons co Kai Lsi Chung. W. ©. Cochran, Arthur Bente, Berard Pian, abn Garang John BG, ss Good ‘Tooroes Lehrer, Jes Darcum, Howatd Keiff, erbert Sur. ising: B. “Thera J John W. Tobe, Tie. Dubie, nd Ces Vou ‘gy fod hepsi in F Mele, RE. X-Rowrke,G, 8. Thee Ie, Probobity wit soto ppt, isn. Wesley, Resting, Mis BWSA. Ashore vrsion acai Prafilip en wate, od tl rer one, Probab: even eroicion 0 pot) hrs 8 pices Way, Nev Yorks Tease, Madtm pb teary an ts appro ie, New York Froenos Moss. Wee otra, Moca Cano the compuscerabee 1B. catching the reds coon sedge Contents Seene BeeReessuRaeeeEEes pans A Mrhany hotles ‘ igrrignr Anat the xing fmm es punta soe sorped an se aeaneesess warese EF hn nope toons @ (2. Tealiog ernmnery no Challenging Problems in Probability L. The Suck Drawer cut, tot pot thet both ire sed.) How sal a he be of Sch fa hears be? (0 Hew Stl te tater of Back fookeis wen? 2. Suveewive Wine “To neonrage Ela promibng tenis cater, le fer fs ben & fie he wine ( lee oe et to a eee eo be Dnyd wit ftir ad the hanpin ema eer champion Fater or chumpioetath-champien. scoring to Elmers hole THe shunpion sa Beer paper thin Eine’ ater, Whi atc show Ee 3. ‘The Ehippumt Jucor | trgemin jar bis cs) members eth of whi ladcpendendy hat potabliy p uf making Ui core decion fn & Td meet Whe He = ein for onch eticn mejor rel) 'A one mun Sry bax prekabiy p Dimabing the cote decom Which jury har Une Ger FEODRUDHE 4, Teiala until Kieat (om the aera, how many meet ee on nb Oe ae 287 in Square common cart ane a ployee rouse «pet Com 8 sma’ of gt fer one te safe af flere Linh age tN ey {inc in arr falls nel Sie aura te ayrrae ens Di does wo ea eu bac ors he ss pena UF he penny Kron the al, whore shana 0 win? ‘chuck sLoek a gesbiog 2am en je ac cami nd ling ome player ay beta one ste ares 2 30-4536. Tee ‘ie ar elle Us lve’ name apes On 80 ec ain, he recoie esentvy on, t,o bee Gime Hs rg ae ie hiown money hacky sthrvine be loam Br stthe. Wht the pages ‘rp Torr asta? culls laser nny cove sero ‘ever mors, but each tich se Ga he opted at 3 eprate e) 7. Curing the Compulsive Gambler Mr, Brow aang tts dl he suit 1 tole pat soe nnd Feet Ti ere Me Bromo paying rl, Kid rca ays tas Bro 320 nea mon hat BOW Hl be en ‘heand of Mle, Hew isthe catering? (Gta Arerin route heels Re 3 egal ely mapa. he papers merce up pid 38 ime Sa od ge is inal fete backs other ops tke) 1B. Torfact Bridge Hand We otien vad ofsnoone ho fs bon dell 8 senes a idee Wid iat (19 of ene sui? Bre is played wi an oediary pack of Sc 13h coh of 4s, nd ch of ger eel 1D) 9. Craps ‘The game of crape las with evo Ae, one of Ans at mad ‘ou popular eambling ge Calc Ihe pide ancited han a