Question

# From a pack of 52 playing cards, all cards whose numbers are multiples of 3 are removed. a card is now drawn in random. What is the probability that the card drawn isi) A face card (King, Queen or Jack)ii) an even numbered red card?

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Solution

## $Totalnumberofcardsinadeck=52\phantom{\rule{0ex}{0ex}}cardswhicharemultipleofthreeare3,6,9\phantom{\rule{0ex}{0ex}}Thesecardsareremoved,sototal3×4=12cardsareremoved.\phantom{\rule{0ex}{0ex}}Leftcardsare52-12=40cards\phantom{\rule{0ex}{0ex}}facecardsinadeckareking,queen,jackinallfoursuits.\phantom{\rule{0ex}{0ex}}Sototalnumberoffacecards=3×4=12\phantom{\rule{0ex}{0ex}}1\right)Sotheprobabilityofdrawingfacecardis\frac{12}{40}=\frac{3}{10}ans\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Evennumberedcardsinredsuitare2,4,8,10.\phantom{\rule{0ex}{0ex}}Sothetotalnumberofevennumberedredcardsare4×2=8\phantom{\rule{0ex}{0ex}}2\right)Sotheprobabilityofdrawingevennumberedredcards=\frac{8}{40}=\frac{1}{5}Ans\phantom{\rule{0ex}{0ex}}$

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