Supposethatapersonisequallylikelytobebornonanyof365daysoftheyear. (a) Forthreepeopleselectedrandomly,explainwhytheprobabilitythattheyallhavedifferent birthdaysis [(365)(364)(363)]~3653. (b) Showthatifatleast23peopleattendasocialparty,theprobabilityexceeds0.50thatat least twopeoplehavethesamebirthday.Stateanyfurtherassumptionsneededforyour solution. (The R function pbirthday(n) givestheprobabilitythatatleast2of n people
Question:
Supposethatapersonisequallylikelytobebornonanyof365daysoftheyear.
(a) Forthreepeopleselectedrandomly,explainwhytheprobabilitythattheyallhavedifferent birthdaysis [(365)(364)(363)]~3653.
(b) Showthatifatleast23peopleattendasocialparty,theprobabilityexceeds0.50thatat least twopeoplehavethesamebirthday.Stateanyfurtherassumptionsneededforyour solution. (The R function pbirthday(n) givestheprobabilitythatatleast2of n people havethesamebirthday.)
(c) Useasimulationtoshowthatif50peopleattendtheparty,theprobabilityis0.97ofat least onecommonbirthday.(Ifresultsseemcounterintuitive,noticehowthenumberof pairs of attendeesincreasesasthenumberofattendees n increases.)
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Related Book For 
Foundations Of Statistics For Data Scientists With R And Python
ISBN: 9780367748456
1st Edition
Authors: Alan Agresti
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