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Amongthe2,598,960possible5-cardpokerhands,howmanycontainthefollowing:a) Atleastonecardthatisnotaheart(complementofallhearts).b) Cardsofmorethanonesuit(complementofallthesamesuit).c) Atleastonefacecard(complementofnofacecards).

User Rahul Sawant
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1 Answer

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26 votes

a) To know the probabilite that atleast one cart is a heart car we have to know that a poker deck have 48 carts and 12 of them are hearts, so the probability that 1 cart is herst will be:


\begin{gathered} p=((12)/(48)+(12)/(47)+(12)/(46)+(12)/(45)+(12)/(44))/(5) \\ p=(0.25+0.255+0.26+0.266+0.27)/(5) \\ p=0.26 \end{gathered}

b) the probability that the carts have more than one suit will be 1 minus the probability that all carts have only one suit so will be:


\begin{gathered} p=1-((12)/(48)\cdot(12)/(47)\cdot(12)/(46)\cdot(12)/(45)\cdot(12)/(44)) \\ p=1-0.001 \\ p=0.999 \end{gathered}

c) we hace 3 face carts for each suit so in total we have 12 face cart, so the probabiliti that a least one is a face cart is tha same as a heart cart so is


p=0.26

User Roy Longbottom
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