probability (1) - indiana university...
Post on 11-May-2020
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Definition
• Afiniteprobabilityspaceisdenotedby(", $) where- ! isafiniteset(thesamplespace),and- " isafunction! → [0,1] (theprobabilitymeasure)suchthat
) "(+)�
.∈0= 1
Wheneverhearing“probability”,makesurethatyouareclearwhattheprobabilityspaceis: whatisthesamplespaceandwhatistheprobabilitymeasureonit.
Probabilitiesofevents
• Let) beaneventofprobabilityspace(", $).Theprobabilityofevent) is
$()) ≔ ∑ $(&)�%∈' .
Examples
• Drawing5cardsfromastandarddeckof52pokercards(Foursuits:clubs,spades,diamonds,hearts.Eachsuithasthirteencards:A,2,3,4,5,6,7,8,9,10,J,Q,K).- WhatistheprobabilityofthefivecardsbeingRoyalFlush(i.e.,same-suit10,J,Q,K,A)?
Examples
• Drawing5cardsfromastandarddeckof52pokercards(Foursuits:clubs,spades,diamonds,hearts.Eachsuithasthirteencards:A,2,3,…,10,J,Q,K).- WhatistheprobabilityofthefivecardsbeingaStraightFlush?Straightflushisapokerhandcontainingfivecardsofsequentialrank,allofthesamesuit,suchasQ� J� 10� 9� 8� (a“queen-highstraightflush”),butnotaroyalflush.
Examples
• Drawing5cardsfromastandarddeckof52pokercards(Foursuits:clubs,spades,diamonds,hearts.Eachsuithasthirteencards:A,2,3,…,10,J,Q,K).- WhatistheprobabilityofthefivecardsbeingaFourofaKind?Fourofakind,alsoknownas quads,isa pokerhandcontainingfourcardsofthesamerankandonecardofanotherrank,e.g., 9� 9� 9� 9� J� ("fourofakind,nines").
Examples
• Drawing5cardsfromastandarddeckof52pokercards(Foursuits:clubs,spades,diamonds,hearts.Eachsuithasthirteencards:A,2,3,…,10,J,Q,K).- WhatistheprobabilityofthefivecardsbeingaFullHouse?Afullhouseisapokerhandcontainingthreecardsofonerankandtwocardsofanotherrank,suchas3� 3� 3� 6� 6�.
Examples
• Drawing5cardsfromastandarddeckof52pokercards(Foursuits:clubs,spades,diamonds,hearts.Eachsuithasthirteencards:A,2,3,…,10,J,Q,K).- WhatistheprobabilityofthefivecardsbeingaFlush?Aflushisapokerhandcontainingfivecardsallofthesamesuit,butnotallofsequentialrank,suchasK� 10� 7� 6� 4�.
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